Custom orthodontic appliance forming apparatus

ABSTRACT

An apparatus for automatically designing and manufacturing a custom orthodontic appliance from anatomical shape data preferably of the lower jaw and teeth of a patient includes a scanner to produce images in three dimensions, a computer that constructs archforms and calculates finish tooth positions, then automatically designs an appliance, preferably including archwires and brackets, to move the teeth to the calculated positions and jigs to place the brackets on the teeth of the patient, and program controlled machines for making the brackets, wires and jigs to the appliance design driven by commands derived from digitized tooth and jaw shape data.

This application is a divisional of the following U.S. patentapplications, each filed Nov. 9, 1992, each by the inventors of thepresent application, each commonly assigned to the assignee of thepresent application, and each containing a specific reference to theother such applications:

Ser. No.: 07/973,973, entitled Method of Forming Custom OrthodonticAppliance, now U.S. Pat. No. 5,431,562;

Ser. No.: 07/973,965, entitled Custom Orthodontic Brackets and Bracketforming Method and Apparatus, now U.S. Pat. No. 5,454,717;

Ser. No.: 07/973,947, entitled Custom Orthodontic Archwire formingMethod and Apparatus, now U.S. Pat. No. 5,447,432; and

Ser. No.: 07/973,844, entitled Method and Apparatus for Forming Jigs forCustom Placement of Orthodontic Appliances on Teeth and Jigs formedTherewith, now U.S. Pat. No. 5,368,478.

FIELD OF INVENTION

The present invention relates to the design, manufacture and use oforthodontic appliances for the straightening of teeth, and moreparticularly, to the automated design, manufacture and use of customorthodontic appliances based on individual patient anatomy and to thediagnosis of patients therefor and the treatment of patients therewith.

BACKGROUND OF THE INVENTION

The orthodontic treatment of patients has as its fundamental objectivethe repositioning or realignment of the teeth of a patient in thepatient's mouth to positions where they function optimally together andoccupy relative locations and orientations that define a pair of opposedand cooperating planar, or nearly planar, smooth arches. The teeth ofthe two arches, the maxillary arch of the teeth of the upper jaw and themandibular arch of the teeth of the lower jaw, when in an optimal orideal position, contact the teeth of the opposite arch along a surfacethat is usually flat or slightly upwardly concave and commonly referredto as the plane of occlusion.

The treatment applied to patients who have been diagnosed as havingteeth insufficiently close to the ideal positions to require orthodonticcorrection includes an initial or rough procedure to overcome the moreserious defects of tooth positioning followed by a finish treatmentdesigned to bring the teeth as closely as possible or practical to theirideal positions. The rough treatment usually involves the movement ofcertain teeth through the use of any of a number of recognizedtechniques performed by an orthodontist, and sometimes procedures suchas the extraction of certain teeth or surgery on the patient's jawperformed by an oral surgeon.

In the finish treatment, the orthodontist applies an appliance, or setof braces, to the teeth of the patient to exert continual forces on theteeth of the patient to gradually urge them toward their idealpositions. The application of the appliance usually involves theattachment of brackets to the teeth, either with the application ofadhesive to the teeth or the securing of bands around the teeth. Thebrackets are usually each provided with a slot through which an archwireis extended. One archwire is provided for the upper teeth and one forthe lower teeth. Typically, the slots in the brackets are of rectangularcross-section and the archwire is of rectangular cross-section. Thearchwire installed in the slots of the brackets interconnects the teeth,through the brackets, and exerts forces on the teeth to translate orrotate them toward a finish position envisioned by the orthodontist.

It has been recognized in the design and application of orthodonticappliances that an ideally designed and installed orthodontic appliancewill present the slots of the brackets in a position to initiallyreceive a preshaped archwire that will elastically deform to exertcorrective forces on the teeth to urge them toward their finishpositions, When in their finish positions, the archwire of the ideallydesigned appliance will no longer be elastically deformed, and will nolonger exert forces upon the teeth. Achieving this objective has beeninhibited by certain problems in the prior art.

One problem presented by the prior art is that current orthodonticproducts are designed and manufactured to average anatomy. As a result,orthodontists are faced with the need to select what they perceive to bethe brackets and archwires of the closest design to those required by aparticular patient, and to modify the designs for treatment of thepatient. Some of this modification may be performed when the applianceis initially installed, but almost inevitably modification is requiredduring the course of treatment of the patient. This modification maytake the form of the replacement of brackets, but most commonly requiresa periodic bending and reshaping of the archwire as the treatmentprogresses. Thus, the treatment of the patient has become a manualfeedback system in which the orthodontist monitors the progress of thepatient's treatment and then readjusts the appliance, usually by bendingthe archwires, to correct the forces being applied to the teeth to bringthe teeth to their ultimate positions, which are less than ideal. As aresult, the patient may be subjected to treatment over a period that islonger than would be necessary if the appliance were initially made tothe optimum design. In addition, the time required of the orthodontistfor implementation of the treatment may be several times greater than itwould be if modification of the appliance were unnecessary. Thus, theorthodontist is able to treat fewer patients and the cost of thetreatment to the patient or to the orthodontist is increased.

Location of the connection points for the appliance to the teeth alsopresents a problem in the prior art. Typically, brackets are bonded tothe teeth and then interconnected by the installation of the archwires.This is done when the teeth are in their realoccluded positions, withthe orthodontist having only a mental vision of where the finishpositions of the teeth will be and where the brackets are to be placedto move the teeth to those finish positions. For more effective use ofthe appliance and to promote ease in cleaning the teeth, theorthodontist prefers to locate the brackets and archwires away from thegums. If they are placed to close to the tips of the teeth, however,they may interfere with the teeth of the opposite arch as the teethapproach their finish positions.

Another problem of the prior art that has inhibited the selection ordesign of an ideal orthodontic appliance for the patient is thedifficulty in arriving at an expression of the ideal finish position ofthe teeth. Orthodontists typically make models of the patient's mouthand, with the models and the aid of x-rays, determine a treatment tomove the teeth to finish tooth positions. This process is time consumingand presents a source of error and inaccuracy. From the measurements andbased on the judgment of the orthodontist, appliance components areselected to implement the prescribed treatment. In reality, thetreatment of patients is in many cases more of an art than a science,with results ranging from poor to excellent, and generally variable.

The need for custom manufactured orthodontic appliances and the use ofautomatic design techniques has been recognized by some, while othershave advocated adherence to standard components and manual techniques inview of a perceived lack of practical custom appliance manufacturing andautomated appliance design systems of the art.

The development of automated custom appliance design systems hasencountered several difficulties. These difficulties have included thetask of developing an automated system that includes reliable andefficient decision making algorithms and techniques for automaticallydetermining an ideal finish position of the teeth. Further, thesedifficulties have included arriving at an expression of appliancegeometry in terms that can be efficiently produced by automatedappliance manufacturing equipment. Furthermore, the prior art has notprovided a way to accurately manufacture an appliance on anindividualized basis in accordance with the appliance design. Anadditional problem in the automated design and manufacture oforthodontic appliances lies in the difficulty in designing the customdesign system to take into account the professionally recognizedparameters and criteria, derived over many years from the knowledge andexperience of the practicing and clinical orthodontist, upon whichdiagnosis and treatment is based,

Accordingly, there is a great need in orthodontics for a practical,reliable and efficient custom appliance automated design andmanufacturing system, and method of providing custom appliances andtreating patients therewith,

SUMMARY OF THE INVENTION

A primary objective of the present invention is to provide a practical,reliable and efficient custom appliance automated design andmanufacturing system and methods of automatically designing customorthodontic appliances and treating patients therewith.

It is a particular objective of the present invention to provide anautomated custom orthodontic appliance design and manufacturing systemthat can be easily and reliably used by practicing orthodontists andthat will make best use of the skills, knowledge and experience that theorthodontist possesses. It is a further objective of the presentinvention to increase the accuracy of the orthodontist's treatment, torender the use of the orthodontist's time more efficient, to eliminatesources of error and guesswork from the orthodontist's treatment ofpatients, and to efficiently, repeatedly and reliably performautomatically the many of the routine steps in the diagnosis,prescription and implementation of orthodontic treatment and in thedesign and manufacture of orthodontic appliances.

It is a further objective of the present invention to improve thepractice of orthodontics by aiding the practitioner in achieving optimalfinish treatment of patients and in more accurately determining andprecisely achieving the finish placement of a patient's teeth. Anadditional objective of the present invention is to provide for theaccumulation of data from individual patients for the analysis of thedata to advance the orthodontic art.

It is still another objective of the present invention to apportion thetasks involved in the design and manufacture of custom appliances mostefficiently between orthodontist and appliance manufacturing facility inaccordance with the scale and other particulars of the individualpractitioner operation.

According to the principles of the present invention, a system andmethod are provided which depart from traditional design and manufactureby designing orthodontic appliances around the anatomy of the individualpatient. Further, unlike current orthodontic products that are designedand manufactured to average anatomy, the orthodontic products of thepresent invention and the methods of manufacturing and using them aretailored to the individual anatomy of the patient.

In accordance with the preferred embodiment of the present invention,there is provided a computerized system and method with which finishpositions of the teeth of a patient are derived from digitizedinformation of anatomical shapes of the patients mouth, an orthodonticappliance is automatically designed from the digitized shape informationand the derived tooth finish positions, machine code is generated forproduction of the orthodontic appliance and communicated to NC machines,and the appliance is automatically fabricated with the machines inresponse to the machine code.

In accordance with the preferred and illustrated embodiment of theinvention, the digitized information is generated from measurements fromthe mouth of the patient, either taken directly or from a model thereof,and preferably includes information of the shapes of the individualteeth of the patient and of the patient's lower jaw.

In the preferred embodiment, the finish tooth position derivationincludes the derivation of one or more archforms, preferably conformingto a skeletal archform defined by the shape of the lower jaw. Theappliance is also configured in accordance with the shape of the derivedarchform, preferably with a mandibular skeletal archform having size andshape conforming to that of the trough of the lower jaw. In thepreferred embodiments, additional archforms are constructed usinginformation of the shapes of the individual teeth and the lower jawskeletal archform to define the positions of the buccal cusps andincisal tips of the mandibular teeth, the marginal ridges of the upperposterior teeth, and the lingual points of occlusion of the upperanterior teeth to position the teeth according to a preferred treatmentplan.

In certain preferred embodiments of the invention, the digitized data istaken by measurements of the patient's individual teeth and the data isreduced to certain landmark data that becomes key to effective andefficient arrival at highly preferred finish tooth positions. Theindividual teeth are arranged on the various derived archforms withmesial and distal contact points of adjacent teeth in contact. Thespacing between the opposite contact points of each tooth are preferablyextracted from a computerized image formed in horizontal plan views ofthe patients teeth. Furthermore, relative locations of the incisal tips,marginal ridges, gingival contact points and the external surfaces ofthe teeth to which the appliance connects, for example, by the mountingof brackets, and which occlude with teeth of the opposite jaw, aredetermined by digitizing vertical profiles of the surfaces of the crownsof the teeth. This data is reduced to define contact points of themandibular teeth with the lower jaw, such as the gingival center points,to define crown axes of the teeth, and other parameters that areamenable to manipulation with a simple and reliable algorithm incalculating the finish positions of the teeth. The landmarks alsoinclude intercusp and inter ridge spacing measurements that provide abasis for prescribing arch expansion treatment with exactness based onthe computer aided calculation of precise finish tooth positions.Further, the tooth position calculations provided improve upon priororthodontic practice by preserving crown long axis inclination anglesand setting the teeth to preferred crown long axis inclination anglesfor population groups according to seed values that are statisticallyimproved upon by the present invention.

In certain embodiments of the invention, images are digitized to producethe tooth and jaw shape data. Preferably, the images include a scannerwhich, in one form, generates a video image from which selected pointsare digitized to produce data from which finish tooth positioning andappliance design is carried out. Alternatively, three dimensionalimaging of the teeth and jaw of the patient is carried out with laser orother scanner to form full three dimensional images of the teeth and jawof the patient. The images may be formed from the patient's teeth andjaw or from a model thereof. Additional data is digitized by takingvertical profiles of the patient's teeth, either by tracing with acomputer the three dimensional images generated with other scanners, orby scanning with a mechanical contact probe or with a non-contact probethe individual teeth of the patient, or model thereof. The data may betaken directly from the patient using CAT scans, MRI, positron emissiontomography or other technique.

Also in accordance with certain embodiments of the invention, the finishtooth positioning includes the establishment of cuspid rise criteria byrigorous calculations made from measured and statistical anatomical dataso that the height of the cuspids and other teeth can be adjustedrelative to each other so that the teeth can be positioned to guide thejaws into proper occlusion. With the present invention, numericalrelationships are provided for cuspid rise that are an improvement ofthe prior art.

In accordance with certain preferred embodiments of the invention, anarchwire forming machine that is responsive to NC code is driven bysignals generated by a computer that reads input data of anatomicalshapes of the patient's mouth, is provided to automatically form anarcuate appliance that interconnects the teeth to move them toward theirfinish positions by rotational and translational forces applied in threedimensions each by the arcuate appliance. Generally, the arcuateappliance is an archwire, and the machine for forming the applianceincludes an archwire forming machine that is responsive to NC code isdriven by signals generated by a computer that reads input data ofanatomical shape of the patient's mouth, preferably of the patient's jawand teeth, derives the tooth finish positions and archwire and bracketdesigns that will move the teeth to the calculated finish positions, andgenerates the machine code to produce the archwire in accordance withthe design. Preferably, the archwires have shapes that conform toarchforms related to the finish tooth positions, particularly to theshape of the patient's lower jaw, and is represented as a series ofsegments of a continuous archwire that each have a constant radius ofcurvature over the length of the segment, and that preferably joinadjacent segments in a smooth transition, with the segments tangentwhere they join.

Further in accordance with certain preferred embodiments of theinvention, a bracket fabrication machine, also responsive to NC code, isdriven by similar signals from a computer responsive to computergenerated finish tooth position calculations and digitized tooth shapedata. Preferably, the brackets have bases that mount on computerdetermined positions on the teeth and have slots to receive archwiresthat are inclined at computer determined angles. The fabrication of thebrackets may include the formation of a slope and/or curvature to themounting surfaces of the bases of the brackets, or, as with theillustrated embodiment, by cutting custom slots in the brackets. In thepreferred embodiment, the design and manufacture of the archwires andbrackets are interrelated so that the curve of the archwire is optimizedto minimize curvature changes and the brackets are optimize to minimizetheir profiles, or the distances from the bases to the archwire slots.The calculations provide a basis for the selection of appropriatebracket blanks for the optimized appliance design.

Additionally, in accordance with other aspects of the invention, one ormore placement fixtures are manufactured from the input data and thecalculated tooth positions for locating points on the teeth, preferablydetermined by the computer, for the connection of the appliance to theteeth, such as for the mounting of the brackets to the teeth. Thefixtures preferably include a set of bracket placement jigs, one foreach bracket that is to be mounted on a tooth, to position and hold thebracket to the tooth so that it can be secured thereto in a precisemounting location. The jigs of the preferred embodiment include a toothprofile or three dimensional surface that fits against the tooth toprecisely locate the jig on the tooth and hold a bracket at a preciseposition and inclination thereon so that it can be secured to the toothwith adhesive.

With the present invention, a custom orthodontic appliance is fabricatedunder the control of a computer directly from data taken from the teethand/or jaw of a patient or a model thereof. The appliance so formed,when connected to the teeth of the patient, moves the teeth of thepatient to precise calculated finish positions without the need for theorthodontist to bend archwires over the course of the treatment. As aresult, the orthodontist's time is conserved, the treatment of thepatient is achieved in a shorter amount of time and the finish positionsof the teeth are more nearly ideal, and consistently so, than thoseachieved with the procedures of the prior art. Furthermore, theappliance fabricating processes result in the generation of data usefulin establishing treatment techniques and criteria that will improve thepractice of orthodontics.

Further, movement of the teeth to the finish positions calculated inaccordance with the present invention results in far more stableplacement of the teeth than with other methods of the prior art whichoften experience movement of the teeth to inferior positions after theorthodontic treatment is terminated.

These and other objectives and advantages of the present invention willbe more readily apparent from the following detailed description of thedrawings in which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1-1F are diagrams illustrating the preferred embodiments of thesystem of the present invention, of which:

FIG. 1 is a block diagram illustrating one preferred embodiment of anautomated system for the design and manufacture of custom orthodonticappliances for the treatment of patients therewith according to theprinciples of the present invention.

FIG. 1A is an elevational diagram of a video graphics image formingembodiment of the data input portion of one embodiment of the scanner ofthe system of FIG. 1.

FIG. 1B is an elevational diagram of a laser scanner version of a threedimensional graphics imaging embodiment of a scanner of the system ofFIG. 1.

FIG. 1C is an elevational diagram of a mechanical tooth profile probescanner version of a two dimensional imaging portion of one embodimentof the scanner of the system of FIG. 1.

FIG. 1D is an isometric diagram of one embodiment of a bracket cuttingdevice of the system of FIG. 1.

FIG. 1E is an isometric diagram of one embodiment of a wire formingdevice of the system of FIG. 1.

FIG. 1F is an isometric diagram of a bracket placement jig formingdevice of the system of FIG. 1.

FIGS. 2-2Z are flow chart diagrams of the preferred methods of carryingout the present invention, of which:

FIG. 2 is a flow chart of one preferred embodiment of the process of thepresent invention performed with the system of FIG. 1.

FIG. 2A is a more specific flow chart illustrating the steps of theinput procedure of automated tooth positioning and appliance design andmanufacturing operation of the process of FIG. 2.

FIG. 2B is a more specific flow chart illustrating the steps of theanalysis and tooth finish position calculating procedure of theautomated tooth positioning and appliance design and manufacturingoperation of the process of FIG. 2.

FIG. 2C is a more specific flow chart illustrating the steps of thecustom appliance design procedure of the automated appliance design andmanufacturing operation of the process of FIG. 2.

FIG. 2D is a more specific flow chart illustrating the steps of thecustom appliance manufacturing procedure of the automated toothpositioning and appliance design and manufacturing operation of theprocess of FIG. 2.

FIG. 2E is a detailed flow chart illustrating the substeps of theidentification data input step of the input procedure of FIG. 2A.

FIG. 2F is a detailed flow chart illustrating the substeps of thepatient history and treatment data input step of the input procedure ofFIG. 2A.

FIG. 2G is a detailed flow chart illustrating the substeps of themandibular bone and horizontal tooth dimension data input step of theinput procedure of FIG. 2A.

FIG. 2H is a detailed flow chart illustrating the substeps of themaxillary horizontal tooth dimension data input step of the inputprocedure of FIG. 2A.

FIG. 2I is a detailed flow chart illustrating the substeps of theindividual tooth vertical profile data input step of the input procedureof FIG. 2A.

FIG. 2J is a detailed flow chart illustrating the substeps of theindividual tooth profile analysis and landmark identification step ofthe analysis procedure of FIG. 2B.

FIG. 2K is a detailed flow chart illustrating the substeps of the cuspidrise calculation step of the analysis procedure of FIG. 2B.

FIG. 2L is a detailed flow chart illustrating the substeps of themandibular preliminary horizontal tooth finish position calculation stepof the analysis procedure of FIG. 2B.

FIG. 2M is a detailed flow chart illustrating the substeps of the bestfit mandibular cusp arch equation calculation step of the analysisprocedure of FIG. 2B.

FIG. 2N is a detailed flow chart illustrating the substeps of thecalculation step of the mandibular tooth finish position on the best fitmandibular cusp arch equation of the analysis procedure of FIG. 2B.

FIG. 2O is a detailed flow chart illustrating the substeps of themaxillary horizontal tooth finish position calculation step of theanalysis procedure of FIG. 2B.

FIG. 2P is a detailed flow chart illustrating the substeps of themandibular archwire plane calculation step of the appliance designprocedure of FIG. 2C.

FIG. 2Q is a detailed flow chart illustrating the substeps of themandibular bracket slot inclination calculation step of the appliancedesign procedure of FIG. 2C.

FIG. 2R is a detailed flow chart illustrating the substeps of themaxillary archwire plane calculation step of the appliance designprocedure of FIG. 2C.

FIG. 2S is a detailed flow chart illustrating the substeps of themaxillary bracket slot inclination calculation step of the appliancedesign procedure of FIG. 2C.

FIG. 2T is a detailed flow chart illustrating the substeps of themandibular archwire and bracket slot in-out dimension calculation stepof the appliance design procedure of FIG. 2C.

FIG. 2U Is a detailed flow chart illustrating the substeps of themaxillary archwire and bracket slot in-out dimension calculation step ofthe appliance design procedure of FIG. 2C.

FIG. 2V is a detailed flow chart summarizing the substeps of the bracketplacement jig shape calculation step of the appliance design procedureof FIG. 2C that is illustrated in more detail in the flowchart of thejig modification step of FIG. 2Z described below.

FIG. 2W is a detailed flow chart illustrating the substeps of the cubicspline curve fitting, spline to circle conversion and tooth placementcalculation subroutines employed in placing teeth on calculatedarchforms in certain steps of the tooth positioning and appliance designand manufacturing operation of FIG. 2C.

FIG. 2X is a detailed flow charts illustrating the NC code generationand slot cutting substeps of the bracket manufacturing step of theprocedure of FIG. 2D, and FIGS. 2X-1 through 2X-4 are more detailedflowcharts illustrating substeps of FIG. 2X.

FIG. 2Y is a detailed flow chart of the substeps of the wire bendingcode generation and wire manufacturing step of the appliancemanufacturing procedure of FIG. 2D.

FIG. 2Z is a detailed flow chart illustrating the substeps of the jigmanufacturing step of the appliance manufacturing procedure of FIG. 2D.FIGS. 2Z-1 through 2Z-6 are more detailed flowcharts illustratingdetails of substeps of FIG. 2Z.

FIGS. 3-3C are illustrations of graphics computer images produced in theinput procedure, in which:

FIG. 3 is a an example of a computer display of a video image generatedby the scanner of the system of FIG. 1 illustrating in a top plan view amandibular model produced by the scanner of the type shown in FIG. 1A.

FIG. 3A is a an example of a portion of a three dimensional digitalimage, illustrated in perspective, and produced by the scanner of thetype shown in FIG. 1B.

FIG. 3B is an illustration similar to FIG. 3A of another portion of athree dimensional digital image produced by the scanner of FIG. 1B.

FIG. 3C is an example of a set of vertical tooth profile images producedby the scanner of FIG. 1C.

FIGS. 4-4E are plan views of the teeth of the patient on tooth placementarchforms at various stages of the tooth position calculation procedureof FIG. 2B, of which:

FIG. 4 is a geometric diagram illustrating a horizontal plan view datainput screen showing diagrammatically the video image of FIG. 3 used asa template, with variables relevant to the digitization of data from themandibular video image marked thereon.

FIG. 4A is a geometric diagram similar to FIG. 4 for the maxillaryteeth.

FIG. 4B is a geometric diagram plotting horizontal mandibular archformscalculated through the analysis procedure of FIG. 2B.

FIG. 4C is a geometric diagram plotting horizontal maxillary archformscalculated through the analysis procedure of FIG. 2B.

FIG. 4D is a horizontal plan diagram showing the maxillary teeth intheir finish positions.

FIG. 4E is a horizontal plan diagram showing the mandibular teeth intheir finish positions and with the custom appliance in place.

FIGS. 5-5P are mathematical calculation diagrams for reference inconnection with spline to circle conversion and tooth placement routinesof FIG. 2W, in which:

FIG. 5 is a horizontal plan diagram illustrating the placement of atooth on an archform equation described in circle segment form.

FIGS. 5A-5J are detailed diagrams of the spline to circle conversion andtooth placement subroutines.

FIGS. 5K-5P are detailed diagrams of the tooth placement subroutine.

FIGS. 6-6I are diagrams of tooth profiles illustrating landmarkdetermination, tooth inclination and vertical positioning, in which:

FIG. 6 is an isometric image of a three-dimensional computerizedrepresentation, similar to FIG. 2B, of a molar showing the locations ofalternative vertical labial-lingual profile planes and tooth profiles.

FIG. 6A is a mathematical tooth profile plot as illustrated on thecomputer screen of a the system of FIG. 1 of a mandibular molar showingselected landmark parameters.

FIG. 6B is a mathematical tooth profile plot, similar to FIG. 6A, of amandibular cuspid or incisor showing selected landmark parameters.

FIG. 6C is a mathematical tooth profile plot, similar to FIG. 6A, of amaxillary molar or bicuspid showing selected landmark parameters.

FIG. 6D is a mathematical tooth profile plot, similar to FIG. 6A, of amaxillary cuspid or incisor showing selected landmark parametersrelevant thereto.

FIG. 6E is representation of a display, similar to FIG. 3C, of an arrayof mathematical tooth profile plots of all of the teeth, angularlyoriented, with landmark parameters marked thereon.

FIG. 6F is representation of a display of an array of mathematical toothprofile plots, similar to a portion of FIG. 6E, of the mandibular teethwith working horizontal placement planes marked thereon.

FIG. 6G is mathematical tooth profile plot, similar to FIG. 6A, of amandibular posterior tooth with relevant dimensional variables forplacement of the tooth marked thereon.

FIG. 6H is mathematical tooth profile plot, similar to FIG. 6B, of amandibular anterior tooth with relevant dimensional variables for theplacement of the tooth marked thereon.

FIG. 6I is mathematical tooth profile plot, similar to FIG. 6H, of a thetallest mandibular tooth.

FIGS. 7-7D are diagrams for reference in connection with the finishtooth position calculation, of which:

FIG. 7 is an elevational diagram of the relationship of the jaws of apatient for illustration of cuspid rise occlusion calculation.

FIG. 7A is an enlarged view of a portion of FIG. 7.

FIG. 7B is a plan mathematical diagram illustrating certain of themathematics of tooth placement on the mandibular offset arch.

FIG. 7C is a perspective diagram illustrating the relationship of thevertical tooth profile planes and relevant horizontal arch planes in thecourse of tooth finish position calculation.

FIG. 7D is a set of related elevational profiles of mandibular andmaxillary teeth showing occlusal and overlap relationships in the courseof tooth finish position calculations.

FIGS. 8-8H are diagrams for reference in connection with the steps ofthe custom appliance design procedure, of which:

FIG. 8 is a diagram similar to FIG. 7D illustrating archwire plane andbracket slot design on positioned teeth.

FIG. 8A is an elevational diagram illustrating a bracket and slotconfiguration in connection with the diagram of FIG. 8.

FIG. 8B is a top view illustrating the relation of a tooth to anarchform by placement routine of FIG. 2W.

FIG. 8C is a tooth profile diagram illustrating the slot in-outdimension calculation.

FIG. 8D is a perspective diagram illustrating the placement of a custombracket onto a tooth with the use of a custom placement jig.

FIG. 8E is a plan diagram of a custom archwire for the appliancerequired to move the mandibular teeth to the finish positionsillustrated in FIG. 4E.

FIG. 8F is a plan diagram illustrating the labial installated applianceon the teeth of the patient in their initial positions.

FIG. 8G is a plan diagram, similar to FIG. 8F, illustrating a lingualappliance installed on the teeth of the patient.

FIG. 8H is an elevational diagram illustrating an orthodontic lingualbracket of the appliance of FIG. 8G.

FIG. 8I is a top view of a bracket having a base slot curvatureconforming to that of an archwire supported therein.

FIGS. 9-9W are diagrams relating to appliance manufacturing steps, ofwhich:

FIGS. 9-9H relate to substeps of the bracket slot cutting codegeneration and bracket manufacturing step.

FIGS. 9I-9W relate to the substeps of the bracket placement jigmanufacturing step.

DETAILED DESCRIPTION OF THE DRAWINGS

The preferred embodiment of the invention provides a system and methodfor designing and manufacturing orthodontic appliances and for employingthe appliances to orthodontically treat patients for the straighteningof teeth. Unlike traditional orthodontic products, however, theappliances resulting from the practice of the present invention aredesigned around the anatomy of the individual patients. It furtherincorporates in its design criteria the parameters and professionaltreatment approaches of the treating orthodontists, and appliesautomated decision making processes in the appliance design that takeinto account the professionally recognized characteristics andanatomical landmarks of the patients.

The overall configuration of the system 10 is illustrateddiagrammatically in FIG. 1. The overall operations of the preferredmethod of the invention are illustrated in the flowchart of FIG. 2.

In accordance with the preferred embodiment of the invention asillustrated in FIGS. 1 and 2, examination of a patient is performed byan orthodontist at the orthodontist's office for the purpose ofassembling the information necessary to determine the patient'scondition, prescribe the appropriate treatment, and specify the type oforthodontic appliance to implement the treatment. The information isthen communicated to a remotely located appliance design andmanufacturing facility where the design of a custom appliance for use inadministering the treatment is carried out with the use of computeranalysis. The appliance design, together with the information necessaryfor the orthodontist to install the appliance on the patient is thentransmitted back to the orthodontist, who installs the appliance andadministers the treatment in accordance with the appliance manufacturesinstructions and his own professional expertise.

In accordance with alternative embodiments of the invention,digitization of anatomical information for computer input is performedeither at the appliance design and manufacturing facility, by theorthodontist at his office, or preferably divided between the two.Similarly, the present invention contemplates the manufacture of theappliance to be performed at either the appliance manufacturingfacility, at the orthodontists office, or preferably divided between thetwo locations and in accordance with the analysis and design provided bythe system of the present invention.

The practice of the present invention involves the use of certain systemhardware, tangible records of information, and communications pathsdescribed below in connection with FIG. 1 and related illustrations, andthe performance of operations, procedures and steps described inconnection with the flowchart of FIG. 2 and related diagrams, all as setforth in detail below.

TERMINOLOGY AND CONVENTIONS

Throughout the description, references are made to tangible elementsillustrated in the drawings and to actions performed by hand and bycomputer. In the description, numbers used to refer to structure orother tangible items illustrated in the drawings of the preferredembodiment appear in conventional form in the text, while numbers thatrefer to method steps in the illustrated flowchart are enclosed inparentheses in the following description. Letter symbols are used torefer to geometric or mathematical representations of variables,parameters, dimensions and values, input into or calculated by acomputer, tie into equations and diagrams illustrated in the drawings,or correspond to computer codes or conceptual items set forth in thedisclosure.

Throughout this description, the various teeth of the patient, up tothirty-two in number, may be identified as T_(JSI), or T(J,S,I), where Jdesignates the jaw (upper: J=U; lower: J=B), where S designates the side(patient's right: S=R; patient's left: S=L), and/designates the tooth byposition relative to the jaw centerline as follows:

I=1: Central Incisor

I=2: Lateral Incisor

I=3: Cuspid

I=4: First Bicuspid

I=5: Second Bicuspid

I=6: First (6 year) Molar

I=7: Second (12 year) Molar

I=8: Third (Wisdom Tooth) Molar

The wisdom teeth are, however, customarily not involved in orthodonticprocedure and usually are not yet present in the mouth of patients oftreatment age. Furthermore, the second molars are often not involved inorthodontic treatment. To simplify the description and drawings,however, these designations are eliminated except where they arenecessary to avoid ambiguity. Instead, the description below statesverbally when it relates to, for example, the lower jaw (thus making useof the J subscript unnecessary) or where it relates to data orcalculations relevant to a particular or either side of a jaw (thusmaking use of the $ subscript unnecessary).

Further, many values are calculated or measured for each tooth I, or foreach of a limited group of teeth, as, for example, the mesio-distalwidth MDW or the mesial and distal extremities M_(X),Y and D_(X),Y as inthe description of step (300) below. Wherever possible, the Idesignation is also eliminated and the description instead describes howthe variables relate to the various teeth. In addition, where somevalues such as MDW discussed above relate to a tooth dimension or thedistance between two points on a tooth (and may be represented by ascaler value in a computer), other values such as the points M_(X),Y andD_(X),Y relate to points M and D, respectively (and may be representedby a pair of X and Y coordinates in a computer). Usually, the subscriptsdesignating the two coordinates are omitted, and where helpful toclarify the description, a single one of the subscripts X or Y may beused, such as with D_(X) or D_(Y), to designate that only the X or Ycoordinate is employed, for example, in a calculation.

SYSTEM CONFIGURATION

Referring to the system diagram of FIG. 1, an orthodontic appliancemanufacturing and patient treatment system 10 is illustrated. The systemcomponents are distributed between two locations, a doctor's office 11,and an appliance design and manufacturing facility 13. At the doctor'soffice 11, a patient 12, who requires orthodontic treatment, is examinedby an orthodontist 14, who makes a diagnosis 15 of the condition of thepatient and of the treatment, if any, needed. The examination involvesthe traditional application of the skill, knowledge and expertise of theorthodontist 14, and results in the preparation of detailed records 16of the anatomy and condition of the mouth 18 of the patient, of thetreatment proposed, and of other information necessary to thepreparation of an orthodontic appliance.

The records 16 prepared by the orthodontist include a physical model 20from a mold of the patient's mouth 18, which includes a mandibular model21 of the patient's lower jaw or mandible 22 and a maxillary model 23 ofthe patient's upper jaw or maxilla 24. The records 16 also includeprescription 27 wherein the orthodontist sets forth a treatment to beapplied to the patient and a result to be achieved by the treatment. Theprescription 27 may also include a specification of techniques that areto be included in the treatment and a designation of an orthodonticappliance to be employed. The records 16 will further includeidentification information 17 and patient history information 19.

In the illustrated embodiment of the invention, the records 16 aretransmitted to the appliance manufacturing facility 13, at which thefinish position of the teeth are calculated and a custom appliance 25 isdesigned and manufactured. The facility 13 is provided with one or moretrained operators 28. In some embodiments, the physical model 20 itselfis transmitted in the information 16 to the facility 13. In such cases,one of the primary functions of the operators 28 is to input digitalinformation 26 from the records 16 into a computer 30a. Another functionis to operate the same or another computer 30b to design the customappliance 25, and to operate NC equipment 38 controlled by one of thesame or another computer 30c to manufacture the appliance 25. Where theinputing, design and manufacture are performed at the appliance facility13, the computers 30a, 30b and 30c may be the same computer 30.

In other embodiments of the invention, the orthodontist 14 digitizesdata from the model 20, in which case the inputing computer 30 islocated at the orthodontist's office 11. In these embodiments, thedigitized information 26, rather than the physical model 20, istransmitted to the appliance facility 13. The analyzing and appliancedesign computer is nonetheless preferably at the appliance facility 13.

The entry of the information into the input computer 30 involves adigitizing of the information 16 to produce the digitized anatomicalinformation 26 in machine readable form for analysis by the analyzingcomputer 30b. The input computer 30 connected thereto by a scanner 33,which, in the alternative embodiments of the invention, includesequipment that employs one or more video cameras, mechanical probes,laser scanners, ultrasonic scanners, moire image scanners or other formsof imaging or measurement hardware that alone, or in combination withother such components, produce anatomical geometric information thatdescribes the patient's teeth and jaw. The images may bethree-dimensional or be made along a plurality of planes or othersurfaces that can ultimately be combined to provide information in threedimensions.

The combined information from the scanner 33 of the illustratedembodiment provides a basis for three dimensional analysis of thepatient's teeth and from which calculations of finish tooth positionscan be made. From the final positional calculations and tooth anatomydata, automatic design and manufacture of the custom orthodonticappliance 25 is carried out. In the illustrated embodiment, the data isimaged in a plurality of differently oriented two dimensional planes inthe computer 30, then mathematically manipulated and combined in thecomputer 30b to construct a three dimensional solution to the toothpositioning and appliance design problems.

In a configuration in which the scanner 33 is connected to a separatededicated inputing computer 30 is herein described, the functionalequivalent of the inputing computer 30 may be included in circuitrywithin the scanner 33 itself.

Preferably, the digital input process utilizes interactive methods bywhich an operator 28 uses a pointing device and digitizer to selectparticularly useful orthodontic parameters from graphics images producedby the scanner 33 on a screen 35 of a display connected to the inputingcomputer 30.

In embodiments where some or all of the extraction of the digitizedanatomical information 26 from the model 20, which may also be deriveddirectly from the mouth 18 of the patient 12, is accomplished by theorthodontist 14 at the orthodontist's office 11, the information 26 isdigitized by the orthodontist 14 then transmitted as part of theinformation 16 to the appliance design center 13. The transmittedinformation 16 is preferably transmitted from the orthodontist's office11 to the appliance facility 13 by modem, but may be transmitted in anyother available manner.

An analysis and design computer 30b, preferably at the appliance designfacility 13, produces an archive diskette 34 that is formatted andwritten with all of the relevant information of the analysis and thehistory and prescribed treatment of the patient 14.

The computer 30b at the appliance facility 13 calculates, based on thedigitized information 26, the final position of the patient's teeth, andthe configuration of the appliance 25 required to move the patient'steeth to this final or finish position. As a result, calculatedinformation for the patient is stored in a patient data file 36. Fromthe calculations the computer 30c produces CNC machine readable code 42for operating NC manufacturing equipment 38 to produce the appliance 25.An instruction document or file 37 is also produced, either by thecomputer 30b or the computer 30c, of information to aid the orthodontist14 in treating the patient 14 with the custom appliance 25.

The manufacturing equipment 38 includes an appliance bracket cutting orforming machine 39 which produces custom brackets for the appliance 25by cutting slots calculated angles and to calculated depths in slotlessgeneric brackets. The machine 39 may also or alternatively shape thesurfaces of the bracket bases. This provides the bracket design optionof torquing the teeth by either the bracket slot or base, as may be bestfor various bracket materials.

The equipment 38 also includes an appliance archwire bending or formingmachine 40 which produces custom shaped archwires for the appliance 25by feeding and bending wire of any one of several available materialsand stiffnesses into the custom archwire shape. The equipment 38 mayalso include a machine for forming patient treatment components andhardware to aid in the manufacture or installation of the appliance 25.In the illustrated embodiment, this includes a machine 41 for the makingof bracket placement jigs, which cuts each tooth crown portion of thetooth profile into a plastic form, along with a superimposed cutout ofthe positioned bracket, for use in accurately installing the custombrackets in their calculated positions on the teeth.

The appliance manufacturing machines 38 may be connected directly to theanalyzing computer 30b or one or more may be connected to a separatemanufacturing equipment controlling computer or machine controller 30c.The computer 30c may be located at the appliance facility 13 or,together with one or more of the appliance manufacturing machines 38, 40or 41, be located at the orthodontist's office 11. In one preferredembodiment of the invention, one manufacturing computer 30c and thebracket cutting machine 40 are located at the orthodontist's office,along with the scanner 33 and input computer 30, which may be the samecomputer as the manufacturing computer 30c, while another manufacturingcentral computer 30c, which may be the analyzing computer 30b, the wirebending machine 40 and the jig forming machine 41 are located at theappliance facility 13. The optimum distribution of the computers 30, 30band 30c and the scanner 33 and appliance manufacturing machines 38, 40and 41 will be determined by the scale of the orthodontist's practiceand the orthodontist's preferences. In the illustrated embodiment, thecomputers 30-30c are IBM PC clones, with Intel 80386 or 80486microprocessors and equipped with 80387 or 80487 math coprocessors,respectively.

Certain components of the system 10 of FIG. 1 are described below infurther detail.

Scanning Assembly 33:

Three steps in the information input procedure (82), described below,involve the inputing into the computer 30, for analysis in digital form,of data concerning the shape of the mouth 18 of the patient 12 and ofthe shapes of the individual teeth therein. In these steps, digitizedimages and measurement data of the mouth 18 of the patient 12,preferably taken indirectly from the model 20, and digitized to form athree dimensional mathematical model of the patient's mouth 18. Themathematical model includes, in the preferred embodiment of theinvention, the definition of certain parameters of the patient's lowerjaw and individual teeth, and may include some information of theinitial position and orientation of the teeth in the mouth 18 of thepatient 12 for evaluating the magnitude of the treatment.

The input information 26 is, in some embodiments of the invention, inputas a full three dimensional image, and then simplified by reducing it toa plurality of curves in a plurality of differently oriented planes orfairly flat curved surfaces, each defined in the independent X-Ycoordinate system of the respective surface or plane. In subsequentanalysis, these planes are oriented, translated and rescaled withrespect to each other in arriving at a derivation of the ideal finishpositions of the teeth and the design of the custom appliance 25. Inaccordance with the preferred embodiment of the invention, curves andpoints on the contours of the jaw and teeth of the patient 12 areexpressed in terms of accepted or generally applicable orthodonticparameters so that manual and automated decision making can combine andcoordinate the best of orthodontic knowledge and experience with theefficiency and precision of computer analysis to minimize the use of theorthodontist's time, shorten the patient's treatment period and optimizethe final treatment result.

The various types of and components of the scanner 33 of variousembodiments of the invention are described below.

Video Scanning Data Input Assembly 43:

One preferred form or component of the scanner 33 includes a videoimaging assembly 43 as illustrated in FIG. 1A. The video imagingassembly 43 includes one or more video cameras 44 which each produce twodimensional images of the patient's mouth 18, preferably by forming animage of the model 20. When two or more are used together, the videoassembly 43 produces stereo images capable of being resolved in threedimensions. In the illustrated embodiment of the invention, a singlevideo camera 44 is employed to produce two dimensional video images of aplan view of the patient's lower or upper jaws 22 and 24, from themodels 21 or 23, respectively, in generally horizontal X-Y planes. Inaccordance with this embodiment, other forms or components of thescanner 33 are preferably employed to produce information in a thirddimension as described below.

Referring to FIG. 1A, the video imaging assembly 43 is showndiagrammatically in side elevation at the appliance manufacturer'sfacility 13. The video imaging assembly 43, in its preferred form, is anoperator-computer graphical interface that includes the video camera 44connected to a video interface board 44a in the input computer 30. Thecamera 44 is mounted on a stand 45 to face downwardly to form a top planview one of one of the halves 21 or 23 of the model 20, shown as themandibular portion 21 in FIG. 3, on a horizontal support 46 attached toa base 45a of the stand 45. The model half 21 or 23 is positioned on thesupport 46 such that the teeth face upwardly toward the camera 44 and sothat the tips thereof lie generally in a horizontal plane that ismaintained at a known fixed distance from the camera 44, so that thescale of the image formed by the camera 44 is known. This may beaccomplished by mounting the support 46 on springs 46a to urge the modelhalf 21 or 23 upwardly against a transparent horizontal plate 45b.

The input computer 30 has connected thereto a pointing device which maybe a mouse 47a or, as shown, a mouse equipped digitizer board 47. Thecamera 44 produces a graphics image display 48 on the screen 35 of thecomputer 30, which an operator 28 may align with the assistance of apositioning grid G (FIG. 4A). With the digitizer 47, the operatorselects points by positioning a curser 48a on the screen 35 with themouse 47a. The selection results in the storage of X, Y coordinate datafor each of the points selected. The points selected, in the descriptionof the preferred process below, correspond to preselected boundarypoints of the teeth and, from the mandibular model 21, the lower jaw.From these top view boundary points, tooth and mandibular jaw dimensionsare calculated. The calculated dimensions are used in analysis steps tocalculate equations for the mandibular bone structure or mandibulartrough MT and to calculate from the trough equation and the calculatedhorizontal dimensions and relative positions of features on individualteeth the finish positions of the teeth.

In the alternative to selecting points from the video image display 48,the same points may be selected in the same manner from a plan viewvideo image of a digitized three-dimensional computerized image of theteeth and jaws, such as an image formed by a laser scanner, moireinterference pattern scanner, ultrasonic scanner, stereo video cameras,or other three-dimensional imaging apparatus. Sectional displays 55a and55b of such a three-dimensional computerized image made with a laserscanner are shown in perspective in FIGS. 3A and 3B, respectively. Sucha laser scanner is described in connection with FIG. 1B below.

Laser Three-dimensional Image Input Assembly 51:

One preferred form or component of the scanner 33 is the laser generatedthree-dimensional image forming assembly 50 illustrated in FIG. 1B.Referring to FIG. 1B, one of the halves 21 and 23 of the model 20 ismounted on a support 51 while laser 52 directs a laser beam 52a onto themodel 21 or 22. The laser beam 52a is reflected and the reflected beamis detected by a sensor 53 composed of a photoelectric pixel array whichuses a triangulation method to convert a change in position on thesensor into a change in distance between the assembly 50 and the model21 or 23 mounted to translate parallel to the model 21 or 23 on asupport 54 so as to scan the model with the laser beam. Equipment forproducing images using laser technology in this manner is commerciallyavailable for forming computerized representations in three dimensionsof manufactured and other objects. An example of equipment suitable forthis purpose are the Cyber Scan™ Measurement System manufactured byCyber Optics Corporation of Minneapolis, Minn. The images formed by suchequipment would preferably include full detailed three-dimensional imagedata of the patient's lower and upper jaws 22 and 24, taken from themodel 20, with the teeth in their original positions. The data iswritten in standard ASCII files by the equipment described and isreadable by the input computer 30a into the digitized information files26.

Illustrated in FIGS. 3A and 3B are two sections of the mandibulardigitized model, and include a section 55a showing the front mandibularincisors T_(BR1) and T_(BL1) of the patient 12, and a section 55bshowing the right mandibular second bicuspid T_(BR5) and first molarT_(BR6) of the patient 12. When such images are rotated to a horizontalplan view, a derivation of the same information that is available fromthe video imager 43 of FIG. 1A may be derived, and points may beselected therefrom for digitization automatically with software, orthrough an operator/computer interactive process as with the videoscanner 43. The three-dimensional image 55 may be rotated into otherorientations for the derivation of other information in various planessuch as vertical tooth profile information that is derived with themechanical scanner 57 described below. Additionally, other computerizedprocedures may be used to automatically derive information from thethree dimensional image 55 with or without intervention or interactionby an operator.

Mechanical Probe Digital Scanner Assembly 57:

The scanner may also include, alternatively or in combination with otherscanning equipment such as the video scanner assembly 43 of FIG. 1A orthe laser scanning assembly of FIG. 1B above, a mechanical probeassembly 57 as illustrated in FIG. 1C. This entire assembly 57 is usedin the illustrated embodiment of the invention in combination with thevideo scanner 43 to derive labial-lingual vertical profiles of theindividual teeth of the patient from the model 20 to supplement jaw andhorizontal tooth dimensional and shape information derived from a videoimage produced by the video scanner 43 from the model 20. Alternatively,portions of this assembly can be used to produce the same informationfrom a three dimensional image 55 produced by equipment such as thelaser scanning assembly 50.

Referring to FIG. 1C, the probe assembly 57 includes a measurement probe60 which is moveable over the individual teeth of the model 21 toproduce an electrical signal that is digitized for computer input ofpoint locations or profiles of the surfaces of the teeth in separate X-Yfor each tooth. In the illustrated embodiment of the process of theinvention, the information 26 preferably derived from the model 21includes the tooth profiles curves PF_(I) in a labial-lingual planeviewed in a mesial-to-distal direction.

The probe assembly 57 further includes a magnetic base 59 upon which ismounted the model 20, and from which extends an upstanding verticalsupport 58 on which the probe 60 is mounted. The probe tip 60a is freelyrotatable about a vertical axis on which its tip lies, while the probeitself is hooked to allow the tip to track recesses in the surfaces ofthe teeth of the model 21. The probe 60 is mounted on the support 58 tomove in X and Y directions in a vertical plane preferably that extendsthrough the support 58 and the probe 60. In this manner, the probe tip60a is positioned to scan the surface of a tooth of the model 21 alongthis plane. The probe 60 is linked to the support 58 through a pair oforthogonal measurement position transducers 61, which respectivelygenerate electrical analog measurements of the positions of the tip ofthe probe 60 along respective ones of the X-Y orthogonal coordinates.The outputs of the transducers 61 are connected to circuitry thatgenerates a sequence of periodic readings of the transducer measurementsof the probe tip positions which are then digitized. These outputs aresent in along lines 61a connected to input computer 30, preferably to aserial port thereof.

In use, a half of the model 20, for example, the mandibular model 21, ismounted upon the magnetic base 59 on a steel surveyor's mount 62 whichslides on the base 59 when lightly urged, but which otherwise holds itsplace thereon for precise positioning. The mount can be raised, loweredor tilted for and for leveling. In operation, the probe 60 is manuallymoved by an operator 28 or automatically to scan the surface of eachselected tooth of the model 21 to produce profile curves PF of a sectionof each tooth as illustrated in FIG. 3C. The profile PF may be generatedby any one of a number of commercially available off-the-shelf CAD/CAMor illustration software packages, such as VERSACAD™ available fromPrime Computers, Inc. of Bedford, Mass. The computer programs describedin the flowcharts herein is written for use with VERSACAD™ in CPL™, theprogramming language of therefor. The video images 63 of the profiles PFare displayed on the screen 35 and the digitized profiles are stored aspart of the input information 26 in non-volatile memory of the computer30.

With the curves such as the profile PF so formed, an operator can, withthe use of the pointing device 47, select, by positioning the cursor onthe formed profile on the screen 35, point parameters of the tooth, thecoordinates of which can be thereby input digitally into the computer30.

Appliance Manufacturing Equipment 38

The manufacturing equipment 38 of the preferred embodiment of theinvention includes: an appliance bracket cutting or forming machine 39that custom forms the bracket bases to mount to the teeth and cutsarchwire slots in the brackets at precise calculated positions andangles; an appliance archwire bending or forming machine 40 thatprecisely bends archwires to a shape that will cooperate with the custombrackets to apply corrective forces to the teeth until they are in theircalculated finish positions; and a bracket placement jig forming machine41 that manufactures bracket placement jigs that conform to the contoursof the patient's teeth, as recorded in the profiles PF. These jigs areused by the orthodontist to precisely place the custom brackets atcalculated positions on the teeth.

The manufacturing equipment 38 is controlled by NC computer generatedprograms based on the data from the digitized input information files 26and the calculated patient data files 36.

Bracket Cutting Machine 39:

Referring to FIG. 1D, a bracket slot cutting machine 39 is illustrated.The machine 39 includes a stationary base 72 on which is fixed a pair ofupwardly extending workpiece support brackets 72a to the top of which ispivotally mounted a workpiece or bracket support 73. On the support, afull set 80a of brackets 80 for the custom appliance 25 is mounted,prearranged in an assembly or cartridge of twenty or twenty-fourbrackets. The support 73 pivots about an axis 73a extending between thebrackets 72a. Connected to the axis 73a is an angular positioning motor74 which positions the support 73, and the brackets 80 mounted thereto,to any angular orientation with respect to the horizontal. The motor 74has an input connected to the computer 30c to set the inclination to theslot inclination angle of the bracket design in response to NC commandcodes.

Also fixed to the base 72 and extending upwardly therefrom is a sawsupport bracket 72b. To the top of the support bracket 72b is a sawdrive motor 75 and a set of three saw blade positioning linear driveactuator 76, including an X-drive actuator 76x, a Y drive actuator 76y,and a Z drive actuator 76z through which a saw support arm 77 issupported to move respectively in the X, Y and Z directions, that is, inan X direction horizontally perpendicular to the axis of rotation 73a ofthe bracket holder 73, in a Y direction horizontally parallel to theaxis of rotation 73a of the workpiece holder 73, and in a vertical Zdirection. The actuators 76 have inputs connected to the computer 30c toreceive positioning signals from the computer 30c to cut arcuate slotsin the X-Y plane of the machine 39 in response to NC commands generatedin accordance with a custom appliance design.

At the remote end of the moveable arm 77 is a slot cutter assembly 77a,drivably linked to the motor 75. The assembly 77a has extendingdownwardly therefrom a rotatable cutter blade drive shaft 77b, which hasfixed to the lower end thereof a circular slot cutter blade 77c. Theblade 77c lies in the horizontal X-Y plane and is of the thickness ofthe slot needed for the thickness of archwire selected. The archwiresare typically rectangular in cross-section so that they are able toexert torque on the bracket, which accordingly will be provided by thesaw blade 77c with a slot of rectangular cross-section. The base of theslot will be cut, in accordance with the command signals from thecomputer 30c, at an angle in the X-Y plane of the machine 39 that istangent to the final curve of the archwire that it will receive. Thebase of the slot will be convex to accommodate the curve of the wire inthe horizontal plane. The base of the slot will be convex to accommodatethe curve of the wire in the horizontal plane. The inclination of thebracket slot is achieved by the angle of the support 73 in response tocontrol signals from the computer 30c. The computer 30c is programmed toaccount for changes in elevation of the bracket 80 due to the offset ofthe brackets from the support axis of rotation 73a.

Wire Bending Machine 40:

The wire bending apparatus 40 is illustrated diagrammatically in FIG.1E. Primary control of the apparatus 40 is preferably by an IBM PCclone, preferably with an 80386 or 80486 microprocessor with a mathcoprocessor, and with motion controller board 65 installed. Thecontroller board 65 is, for example, an MC300 Motion controller 3-axiscard manufactured by Motion Engineering, Inc. The MC300 is a dedicatedmotion control card which sends and received signals to and from MC-OLSstepper interfaces 66a and 66b. MC-OLS stepper motor interfaces 66a and66b send control signal commands to the stepper motor power supplies 67aand 67b, such as Compumotor S-Drive stepper power supplies 011483D,regarding rate and direction of motion of the motors.

The power supply 67a has an output connected to wire feed rollers 68,positioned on opposite sides of a wire guide 68a, which guides archwire69 to feed it from a continuous coil supply. The power supply 67b has anoutput connected to a wire bending roller assembly or wire anvil 70.

The controller 66b additionally is adapted to receive feedback signalsregarding position from a disc encoder 70a, such as a Dynapar/VeederRoot #E1000A76500, which monitors the position of wire forming roller70b, providing closed loop control of a wire bending roller 70b. Theroller is driven by a wire anvil motor 70c, such as a Compumotor #S/SX57-102, through a drive screw 70d, such as an Industrial Devices Corp.Electric cylinder #X995A-2-M56-MT1-200-PS. The screw 70d converts theangular position of the motor 70c into linear motion of the roller 70bto deflect and bend the wire 69 as it is fed through the guide 68a bythe rollers 68.

By coordinating the anvil 70 and the wire feed 68, formed archwires 64of any planar shape are fabricated. The rollers 68 pinch the wire,forcing it to advance into the anvil 70. The roller 70b of the anvil 70moves up and down varying the radius and thus controlling the radius towhich the wire is permanently deformed. If the formation of archwireswith inflection points, that is that have bends in opposite directions,a second anvil would be provided opposite the wire 69 from the anvil 70and controlled in synchronism therewith.

A wire position sensor 71 is provided that inspects the finishedarchwire by comparing the width of the formed wire 64 to the desiredwidth. The sensor 71 is mounted with respect to the anvil 70 and feedrollers 68 to detect the position of the formed archwire 64 when it isat the end of its forming cycle. This measurement provides a feedbacksignal that provides compensation for material property variations thateffect the formed shape and the amount of overbending required. Thesensor 71 sends information back to the computer 30c as to whether thewire 64 is acceptable or over-bent or under-bent. If the wire is eitherover or underbent, the computer 30c calculates the correction requiredand incrementally modifies the signals through the interfaces 66a and66b to provide compensation to progressively correct successivearchwires 64 until the result of the signal from the sensor 71 is deemedacceptable by the computer 30c.

Bracket Placement Jig Forming Machine 41:

The bracket jig forming equipment 41 is preferably a standard NC millconfigured as illustrated in FIG. 1F. The machine 41 includes thestandard mill 81, having a downwardly projecting rotary tool head 81a onwhich is mounted an endmill tool 81b of, for example, 0.020 inches indiameter, where 0.022 inch archwire is used, and, for example 0.016inches in diameter where 0.018 inch archwire is used.

The mill 81 is either connected to an controller which will have beenloaded with CNC program code 42 prepared by the computer 30c or will bedirectly connected to the computer 30c. The mill 81 is provided with atool support 81c to which a set of circular ABS plastic jig blanks 83,usually twenty or twenty-four in number, are fed by a feeding mechanism81d, equipped with a magazine 81e of the sets 83a of jig blanks 83. Thetool head 81a is moveable vertically to bring the tool 81b into contactwith the blanks 83 and horizontally in the X-Y directions in accordancewith the tool path instructions from the code 42.

GENERAL OPERATIONS AND PROCEDURES

In the preferred and illustrated embodiment of the invention, theoverall configuration of which is illustrated diagrammatically in FIG.1, the full custom system 10 is operated to produce the orthodonticappliance 25 based on the individual anatomy of the patient 12. Onepreferred method of the invention is represented by the operations andprocedures illustrated in the flowchart of FIGS. 2.

The method of the present invention, in its preferred embodiment,includes three general operations. The first operation, is (85) apatient evaluation operation performed by the orthodontist 14 at thedoctor's office 11 on the patient 12. This operation includes thetraditional professional diagnosis and general prescription oftreatment. According to the present invention, the evaluation operation(85) is followed by (87) a computer aided analysis and appliance designand manufacturing operation performed, preferably at least in part, atthe appliance facility 13 to produce the custom appliance 25, and inturn followed by a patient treatment operation (89), which includestreatment of the patient 12 by the orthodontist 14 at the doctor'soffice 11, with the installation and use of the appliance 25.

(85) Patient Evaluation Operation

Referring to the system diagram of FIG. 1 and the flow chart of FIG. 2,the orthodontic evaluation operation (85) is performed at a doctor'soffice 11. The operation (85) includes the procedures (90) of theexamination of a patient 12, (91) the preparation of the model 20 of thepatient's mouth and teeth, (92) the prescription by the orthodontist 14of treatment, (93) and communication the appliance facility 13.

The examination procedure (90) the patient 12, who requires orthodontictreatment, is examined by an orthodontist 14, who makes a diagnosis 15of the condition of the patient and of the treatment, if any, needed.Based on the diagnosis 15, the orthodontist or doctor 14 assembles theinformation 16 that is necessary to implement the prescribed treatment.

In assembling the information 16, the orthodontist 14 (91) prepares amodel of the patient's mouth 18, usually a physical model 20 from a moldof the patient's mouth, in its initial condition at the time of thediagnosis 15. The model 20 includes the mandibular model 21 of thepatient's lower jaw or mandible 22 and the maxillary model 23 of thepatient's upper jaw or maxilla 24.

Then, further based on the diagnosis 15, the orthodontist 14 (92)prescribes a particular treatment and generates a prescription 27 in atangible record form.

The orthodontist 14 then (93) communicates the information 16, forexample, by transmitting the model 20, the prescription for treatment27, a record of information 17 identifying the doctor 14 and the patient12, together with information 19 containing statistical and historicdata of the patient 12, to an appliance design facility 13, at someremote location. At the appliance design facility 13, the information 16is digitized and input into the computer 30 for analysis.

Alternatively, the orthodontist 14 may convert the information 16 todigital computer readable form and transmit the digitized information tothe appliance design facility 13. In this alternative, the system 10would be configured with the input computer 30 located at theorthodontist's office 11, and the orthodontist 14 or assisting personnelwould perform portions of an data input procedure (94) described below.

(87) Analysis, Design and Manufacture Operation

When the information 16, which includes, for example, the model 20, theprescription 27 and the information 17 and 19, are received either atthe appliance system manufacturer 13 or is ready to be digitized at theorthodontist's office 11, (87) an analysis, finish tooth positioncalculation, and orthodontic appliance design and manufacturingoperation is begun. In the operation (87), the information 16 isprocessed and the custom appliance 25 for moving the patient's teeth toan optimum final or finish position in accordance with treatmentprescribed by the orthodontist 14 is produced.

The operation (87) includes the procedures of (94) inputing into acomputer the information 16 from the orthodontist 14, in digital form,(95) analyzing with the aid of computer 30b the input digitizedinformation to arrive at the finish position of the teeth, (96)designing with a computer a custom orthodontic appliance in accordancewith the computer analysis, (97) manufacturing the custom appliance 25in accordance with the computer assisted design with the aid of computercontrolled machinery, and (98) communicating the custom appliance 25 andaccompanying instructions to the orthodontist 14.

In accordance with certain embodiments of the present invention, some orall of the appliance manufacturing step (97) can be performed at thefacilities 11 of the orthodontist 14, in which case the communicatingstep (98) would involve the communication of machine readable code, inlieu of some or all of the completed custom appliance 25, from thedesign facility 13 to the orthodontist 14.

(94) Input Procedure:

In the input procedure (90) is illustrated in the flowchart of FIG. 2A.In the procedure (94), the received information 16 is input, in theillustrated embodiment by operator 28 at the design facility 13, into acomputer 30 in digital form. Even where the inputing is performed byoperator at the design facility 13, some information 16, such as theinformation 17 and 19, may be supplied by the orthodontist 14 in machinereadable form and input directly into the computer 30. The inputprocedure (94) includes five steps (100)-(500), the substeps of whichare described in detail in connection with the flowchart details ofFIGS. 2E-2I below. The steps of the input procedure (90), in theillustrated embodiment, also include certain substeps that are part ofthe function of the analysis step (92) but are more convenientlyperformed at the time of the information is entered into the computer.

The input steps (100) and (200) involve the entry of backgroundinformation assembled by the orthodontist 14. In the input steps (300),(400) and (500), tooth and jaw positions and profiles are defined interms of orthodontic parameters and landmarks that can be later analyzedby computer to best implement the orthodontic knowledge, skill andexperience embodied in the prescription 27 and of the orthodonticprofession while efficiently automatically producing a optimum result.These steps of the input procedure (90) include:

(100) The inputing of the doctor-patient identification information 17in digital form into the computer 30a:

This information is used to identify the records of the patient and theproducts produced.

(200) The inputing of patient background information 19 in digital forminto the computer 30a:

This information is used in part in the calculating the finish positionof the patient's teeth in accordance with genetic characteristics. Sexand race, for example, are used to assign certain seed values such asthe inclination of the axes of the individual teeth of the patient 12 toan arch plane in step (625), which is used to determine an offset fortips of the teeth from the jaw bone or gum line.

This information also includes diagnostic determinations and treatmentoption decisions made by the orthodontist 14, such as determinations toextract teeth, or employ optional treatment norms.

(300) The inputing into the computer 30, from a top view image of thepatient's mandibular model 21, the mandibular jaw shape and toothdimensional information:

In implementing a treatment to correct the tooth alignment of thepatient 12, the mandible 22 is the logical starting point because it isa solid bone and has relatively little pliancy. By contrast, the maxillaor upper jaw 24 is composed of segments held together by sutures whichdo not fuse until mid or late teens. Furthermore, these sutures can beseparated by the orthodontist even after the point of initial fusion bysimple and commonly known clinical techniques. These anatomical factorsrequire that the orthodontist 14 make relatively small changes in themandibular bone 22 and the preponderance of skeletal changes in themaxilla 24. For this reason, the position of the mandibular trough MTtherefore taken as a constraint on the positions of the roots of thelower teeth.

In step (300) information is input for use, in part, to define from thepatient's lower jaw bone the shape of the mandibular trough MT, whichserves as the first constraint in arriving at the finish position of theteeth. In one embodiment, this is accomplished by superimposing apredefined grid G on a video or graphics image of the mandibular trough(from FIG. 3) in the manner illustrated in FIG. 4. In addition, thedistances between the mesiodistal extremities, or mesiodistal widthsMDW, that is, their contact points with adjacent teeth, in a horizontalplane, are input. These determine the total length of the dental archand the relative center-to-center spacings of the teeth along the arch.

A mandibular trough equation MTE is derived, and may be converted to asymmetrical equation SMT. As a starting point toward calculating finishtooth position, the mesio-distal widths of the mandibular teeth aremathematically placed on the trough equation. This is explained morefully below in connection with FIG. 4.

In the above and in many archform calculations below, a cubic splineequation form is used initially in fitting a curve to data points, thenconverted to a circle segment equation that provides advantages in theanalysis and design process and in the final calculations needed tooperate NC manufacturing equipment. This is explained below inconnection with FIGS. 5 et seq.

Measured initial contra-lateral cusp spacing data are generated for useby the orthodontist 14 in evaluating the custom design and treatmentparameters resulting from the final calculations below.

In some embodiments, horizontal profile data of the lower jaw may beinput in this step, additional landmarks in the horizontal plane may beidentified, or full three-dimensional images of the teeth and lower jawmay be made, for example, as discussed in the descriptions of FIGS. 1ACabove.

(400) The inputing into the computer 30, from a bottom view image of thepatient's maxillary model 23, maxillary tooth dimensional information:

The shape of the maxilla, which is made of a segmented bone, is avariable capable of being altered orthodontically in response to finaltooth position calculations as set forth below. Therefore, its initialshape and initial maxillary tooth position is relevant only inevaluating the feasibility of the amount of alteration required and thetype of treatment to be used.

In step (400), information is input into the computer 30c of maxillaryjaw shape and tooth dimensional information from the maxillary model 23.This information is used in part to determine the mesiodistal widths MDWof each upper tooth, in a horizontal plane, and to determine the totallength of the dental arch and the relative center to center spacings ofthe teeth along the arch.

Measured initial contra-lateral cusp and central groove/fossa spacingdata are generated for use by the orthodontist 14 in evaluating thecustom design and treatment parameters resulting from the finalcalculations below.

As with step (300) above, in some embodiments, horizontal profile dataof the upper jaw may be input in this step, additional landmarks in thehorizontal plane may be identified, or full three-dimensional images ofthe teeth and lower jaw may be made, for example, as discussed in thedescriptions of FIGS. 1A-1C above. In these embodiments, techniques suchas those described in step (500) may be employed in the horizontal planein steps (300) and (400).

(500) The inputing of individual tooth elevational profile informationfrom the two halves of the model 20:

The tooth profile information can be generated using computer analysisor interactive computer imaging from three-dimensional images, ifemployed, as illustrated in FIG. 3A formed with scanners such asillustrated in FIG. 1B, or with the use of the probe assembly 57 of FIG.1C from the physical model 20 of the jaw. Use of the probe assembly 57is herein described.

Rapid reduction of tooth shape information to important dimensions andlandmark data for efficient and realizable calculations of finish toothposition is achieved by imaging carefully selected profiles of theteeth. Profiles are produced by outlining the tooth crown surfaces alonga vertical plane or other similarly oriented surface that extends in alabial-lingual direction generally perpendicular to the arch of theteeth in the respective jaw. For the single cusp anterior teeth, thissurface is generally a surface bisecting the tooth and through the crownlong axis CLA of the tooth. For multiple cusp teeth, the same generallyapplies except modification or displacement of the surface isintelligently made on some teeth to pick up the highest cusp or amarginal ridge that is relevant to development of the proper occlusion.

For most calculations, as set forth in the detailed explanation below,the tooth features profile can be assumed to be on a plane through thetooth centerline, even when they are not. With the features selectedherein, such assumptions result in errors that are still much smallerthan those accepted in conventional methods. In other calculations, theprecise position of a feature must be considered, and provision for suchconsiderations are made in the certain embodiments of the invention.

For each tooth, profile data is taken in separate X-Y coordinates thatrelate only to the selected surface or plane. In the course of theanalysis and calculation of finish tooth position, these planes areseparately translated and reoriented with respect to those of the otherteeth and those of the trough and archforms, in several steps, until theultimate interplane relationships are established,

(95) Analysis and Tooth Positioning Procedure:

The computer analysis procedure is illustrated in the flowchart of FIG.2B. In the computer analysis procedure (95), the digitized informationinput by the input procedure (94) is analyzed to calculate the finishposition of the teeth, so that the custom appliance 25 can be designedin computerized design procedure (96) and manufactured in computercontrolled manufacturing procedure (97). The analysis procedure (95)includes six steps and subroutines (600)-(1100), the substeps of whichare described in detail in connection with the flowchart details ofFIGS. 2J-2O below. These steps include the following:

(600) The dental analysis step in which the orthodontic landmarks of theteeth are identified:

A minimum number of points on the tooth profiles are selected that aresufficient for determining the contact points between teeth that arerelevant to finish tooth position calculation and appliance design.These points are selected such that the calculations made from them arerelatively insensitive to measurement errors in the input of the data instep (500). From the selected points, for each tooth, other parametersare derived, including an incisal center point ICP, a gingival centerpoint GCP and the crown long axis CLA through the ICP and GCP, asexplained below in connection with step (600) and FIG. 6 et seq.

In order to determine the relationship between the crown long axes andarchwire planes, twenty-four of each crown type were removed from a setof orthodontic casts and sectioned along the mid-sagittal plane. Thesecrowns were then mounted and projected at twenty times magnification onan optical comparator. Tracings were then made of these profiles. As aresult, a procedure was determined for use to establishing the crownlong axis inclination angles to produce the desired occlusion, and seedvalues were tabulated that and correlated with data such as the sex andrace of the patient as entered in step (200). As a result of thisanalysis, preferred crown long axis inclination angles are produced withthe present invention that are an improvement over the facialinclination angles employed in the prior art,

From the tabulated data, angles of inclination LAIs of the crown longaxes CLAs of each of the teeth of each jaw are set relative to the planethat contains the mandibular trough equation MTE, This plane is parallelto a facial axis plane FAP used in clinical studies through a clinicallydefined facial axis FA of a tooth. These LAIs are later used todetermine the horizontal offsets from the MTE of the tips of the lowerteeth in step (1000) below, as well as the maxillary tooth placement instep (1100). The rotation of the inclination angle places new Ycoordinates of each of the tooth profile planes established in step(500) parallel, and the X axes of these planes parallel to the sameplane but of with their relative horizontal orientations and relativevertical positions yet to be determined. Once the teeth are rotated totheir finish inclinations, precise crown heights, incisal and cusp tiplocations, and other points and contours of the tooth surface areprecisely defined for intertooth contact and appliance design andpositioning calculations.

As an example, for the maxillary bicuspids and molars, a marginal ridgeelevation MRE is determined for later use in calculations relativefinish positions of the upper and lower teeth,

(700) The cuspid rise determination step in which the occlusion of theupper and lower teeth is defined:

The orthodontist 14 will have selected the technique to be used to guidethe teeth of the patient into occlusion as the jaws come together,Depending on the selected occlusion technique, either all or part of theocclusion is brought by a rise of the cuspids above that of the otherteeth, to thereby initiate contact between the upper and lower teethwhich aligns the two arches as the jaw closes. Most orthodontists preferto accomplish this with the rise of the cuspids.

From anatomical studies, data is employed and the amount of cuspid rise,or other cusp rise if selected, that is necessary to clear the buccalcusp height BHC of the teeth, which is determined from the landmark dataof step (600).

(800) The mandibular tooth placement step in which the plane of themandibular teeth is defined and the teeth are positioned with respect tothe mandibular trough:

The step (800) accomplishes the preliminary mathematical construction ofthe mandibular occlusion. This step first calculates the positions ofthe mandibular teeth to place their tips in an occlusal plane pendingfinal refinement of the placement.

The starting point for the mandibular tooth placement is to assume toothpositions that place the teeth with their crown long axes CLAsintersecting the plane of the mandibular trough on the mandibular troughequation MTE. This satisfies the condition that the mandibular teeth areset in the bone of the lower jaw. The CLAs of the teeth are alsoinclined at the seed value angles LAIs established in step (600).

Next, the positions of the teeth are adjusted vertically to place thetips of all of the mandibular teeth, except the cuspids, in the sameplane. The tips of the mandibular cuspids are set to extend above theplane of the tips of the other mandibular teeth by a distance accordingto the cuspid rise criteria selected, preferably by setting the distanceequal to one third of the total cuspid rise, as calculated in step(700).

Then, a horizontal OFFSET from the MTE, generally in the labialdirection, is calculated trigonometrically for each mandibular toothfrom its crown height above the mandibular trough and its long axisinclination angle LAI. This calculation results in a mandibular troughoffset equation MO, which is an outward radial expansion of the MTE. TheMTE was defined in the form of a series of circle segments in step(300). The expanded MO equation is a discontinuous arch constructed byadding the respective OFFSET of each tooth to the radius of the circlesegment of the MTE with which the midpoint of the width of the tooth isassociated.

The teeth are then placed on the offset equation MO beginning with theplacement of the central with its mesial contact point on the mandiblecenterline and the tooth midpoints on the MO. Then moving distally, theremaining teeth on the same side of the mandible are placed on the MOwith their mesial contact points MCP in contact with the distal contactpoint DCP of the previous tooth. The same procedure is employed for theteeth on the other side of the mandibular arch.

An alternative further refinement would consider the vertical positionon the teeth of their widest points and, considering the also theinclinations of the teeth, make a trigonometric adjustment so that thetooth contact points are spaced by the tooth widths MDW at the height oftheir actual widest points, rather than assuming the teeth contact inthe plane of their tips.

(900) The best fit cusp step in which the best fit equation is derivedfor mandibular arch:

In this step, a continuous curve is derived using statistical methods toproduce a best fit buccal cusp equation BFBCE from the disconnected linesegments of the MO. This is also illustrated in FIG. 4A. In theembodiment described below, a Bezier equation is used. A cubic equationis then generated from resulting data points that define the best fitequation. The cubic equation of the BFBCE is then converted to circlesegment form as with the MTE above.

(1000) The mandibular teeth placement step in which the positions of themandibular teeth are calculated for placement on the best fit archequation:

The positions of the lower teeth are then recalculated to move the teethhorizontally, parallel to the MOC, such that the incisal center pointsICP lie on the BFBCE. For incisors and cuspids, the ICPs are the tips ofthe teeth in the profile planes of steps (500) and (600). For thebicuspids and molars, the ICPs are the buccal cusp tips of the teeth.For purposes of placement of the teeth on the BFBCE or other archform,the ICPs are assumed to lie midway between the mesial and distal contactpoints of the respective teeth. Accordingly, tooth placement is achievedby moving the teeth normal to the circle segment associated with theseICPs. This recalculation of position has the effect of moving the rootsof the teeth normal to the arch associated with their ICPs, eitherlabially or lingually, such that their ICPs fall on BFBCE, when viewedfrom above.

This placement is the finish position of the mandibular teeth.

(1100) The maxillary placement step in which the maxillary arch isderived for occlusion with the placed mandibular teeth:

This step fits the positions of the maxillary teeth to the alreadypositioned mandibular teeth. The maxillary teeth have not yet beenpositioned with respect to any equation, but the inclination angles oftheir dimensions and crown long axes CLAs have been determined in step(600). This positioning involves setting the tips of the maxillary teethon the BFBCE, with certain modifications to the equation and theplacement criteria to account for the way the different types of teethocclude.

In adjusting maxillary tooth positions, the cuspids, the anterior teethand the posterior teeth are treated separately to bring their relevantcontact surfaces into three different respective arches that are thenaligned relative to each other.

Since the anterior teeth do not occlude incisal edge to incisal edge,the BFBCE is modified to take into account the distance from the BFBCEto the labial contact points of the mandibular incisors and laterals,plus a horizontal or labial clearance, with the maxillary teeth. Thisdefines the points of occlusion with the maxillary anteriors, at theintersection of their lingual surfaces with the plane of occlusion MOC.These points lie in a maxillary anterior contact arch form MAAF. Thisequation is calculated by expanding the BFBCE, by enlarging the radii ofthe circle segments of which it is made up, to account for these toothdimensions and the clearances.

The vertical positioning of the maxillary anteriors and cuspids is thenperformed based on the vertical occlusion methods that have beenprescribed, establishing an overlap for the incisors and cuspid rise asdetermined in step (700). This defines the vertical position of themaxillary cuspids and anteriors with respect to the MOC, and therebydefines the incisal overlap or overbite.

Placement of the maxillary posterior teeth places the intersections ofthe marginal ridges and the central grooves from steps (400) to (600)the cusps of the mandibular teeth with which they will occlude. Themaxillary tooth movements needed to achieve this occlusion are appliedto calculate a central groove marginal ridge arch form CGMRAF bymodifying the BFBCE. The cusp tips of the maxillary cuspids are placedbetween the archforms of the incisors and of the posteriors, forexample, by averaging the distance from the BFBCE to the MAAF and to thebuccal cusp of the first maxillary bicuspid, by placing the cuspidmesial and distal contact points in contact with the adjacent teeth, bycalculating a clearance as was done for the incisors or by some othercriteria. The archforms for the maxillary tooth placement areillustrated in FIG. 4B.

The vertical positioning of the remaining teeth takes into account theocclusion and other prescription information input in step (200). Theremaining calculations are set forth in detail below.

(96) Appliance Design Procedure:

The appliance design procedure (96), as illustrated in the flowchart ofFIG. 2C, calculates the dimensions of the appliance components in a formcapable of being translated into NC codes for operating NC machinery forproduction of the appliance components, such as the brackets andarchwires and also placement jigs for installing the brackets in theproper positions on the teeth of the patient. In the appliance designprocedure (96) includes the following steps (1200) through (1800), whichare further illustrated in the detailed flowcharts of FIGS. 2P-2V:

(1200) The mandibular archwire plane step in which the plane of thearchwire for the mandibular teeth is defined in relation to the teeth ofthe mandible:

Where labial brackets are to be applied, as illustrated in FIG. 8, aplane is selected for the mandibular archwire that avoids interferencewith the mandibular archwire and brackets with the maxillary teeth,which overlap on the labial side of the mandibular teeth. Where lingualbrackets are to be applied, this step is performed to define a maxillaryarchwire plane to avoid interference between the lingually mountedmaxillary archwires and brackets with the mandibular teeth that overlapon the lingual side of the maxillary teeth.

This step involves the selection of the archwire plane and defines it inmathematical relation to the MOC. Once defined, the bracket positions onthe teeth are determined such that the archwire slots will lie withinthe dimensional limits of the bracket. Where possible, it is preferablethat the archwire lie in a literally flat plane and be symmetrical aboutthe midline of the arch. As such, the archwire will be properly shapedfor installation with either side facing upward.

(1300) The mandibular slot inclination step in which the angles of theslots of the mandibular tooth brackets of the appliance are calculated:

The slot inclination angle for the mandibular brackets is calculatedfrom the angle between the mandibular archwire plane and the angle ofthe mandibular tooth surface to which the base of the bracket is to bemounted. The slot inclination angle may be achieved by cutting the fullangle into the slot, by inclining the bracket base, or by both of thesemethods.

(1400) The maxillary archwire plane step in which the plane of thearchwire for the maxillary teeth is defined in relation to the teeth ofthe maxilla:

The maxillary archwire plane in the case of labial appliances, and themandibular archwire plane in the case of lingual appliances, has fewconstraints on its position and may be selected based on cosmeticconsiderations. It is usually selected as a plane midway on the crown ofthe maxillary teeth. It is therefore normally not parallel to themandibular archwire plane. Once defined, the bracket positions on theteeth are determined such that the archwire slots will lie within thedimensional limits of the bracket.

(1500) The maxillary slot inclination step in which the angles of theslots of the maxillary tooth brackets of the appliance are calculated:

The slot inclination angle for the maxillary brackets is calculated fromthe angle between the maxillary archwire plane and the angle of themaxillary tooth surface to which the base of the bracket is to bemounted. The slot inclination angle may be achieved by cutting the fullangle into the slot, by inclining the bracket base, or by both of thesemethods.

(1600) The mandibular archwire and bracket in-out dimension calculationstep in which the slot depth and bracket geometry is calculated for themandibular tooth brackets:

For each bracket, the deepest and shallowest slot depths is determinedto develop a window into which the archwire must pass, as illustrated inFIG. 8A. Then the smoothest archwire curve that will pass between thedepth limits is determined. The smoothest curve is considered to be onewith the least variation in radius changes along the curve, andpreferably with no inflection points. A cubic spline equation is used tofit the points and the equation is then converted to one of circlesegment form.

(1700) The maxillary archwire and bracket in-out dimension calculationstep in which the slot depth and bracket geometry is calculated for themaxillary tooth brackets:

As with the mandibular slot depth calculations, for each maxillarybracket, the deepest and shallowest slot depths is determined to developa window into which the archwire must pass. Then the smoothest archwirecurve that will pass between the depth limits is determined. Here to,the smoothest curve is considered to be one with the least variation inradius changes along the curve. A curve with no, or the least number ofinflection points is preferred. A cubic spline equation is used to fitthe points and the equation is then converted to one of circle segmentform.

(1800) The bracket placement jig designing step in which placement jigsare designed for use in properly positioning the custom designedbrackets on the patient's teeth:

After the brackets and archwires are completely defined as in the abovesteps, with the depth and angle of the slots finalized for in thepositioning of the brackets on the teeth and the shape of the desiredarchwires are described mathematically, bracket placement jigs aredesigned that will be used to assist the orthodontist in placing thebrackets at the proper locations on the teeth. The designing of thejigs, in the preferred embodiment, is carried out in the software thatgenerates the NC machine code in the performance of the jigmanufacturing step (3500) below. This deferring of the jig design allowsfor consideration of appliance hardware modifications that may be madein the course of the bracket and archwire forming steps (3000) and(3200), respectively.

The provision of the bracket placement jigs furthers a goal of thepractice of orthodontics to treat cases to occlusal perfection with theleast amount of effort, discomfort and time expended. The portion ofthis goal that can be accomplished by appliance design and manufacturehas been described above. While the individualized appliance geometriesthus defined will be fabricated, the ability to place the bracketportion of the appliance system on the teeth with sufficient accuracy toallow the appliance system to deliver the desired orthodonticrelationship, heretofore not realized clinically, is provided asfollows:

The brackets are placed according to the three criteria:

1. Height: The height is established so that the appliance causes theupper and lower teeth to contact each other in the prescribed manner.

2. Mesio-Distally: The mesio-distal location is established so that themesial and distal ridges of the teeth are parallel to the archform forthat patient.

3. Long Axis: The bracket is aligned relative to the long axis of thetooth so that the appliance system tips the tooth to the desired anglerelative to the archwire.

From the vertical profile data of step (500), and horizontal or threedimensional profile data of steps (300) and (400), the shape and size ofeach tooth is extracted, including particularly the profile in amesio-distal view at the height of contour or along a planeperpendicular to the greatest prominence of the central developmentallobe of each tooth. Additionally, the geometry of the archwire slot hasbeen accurately related to the respective teeth. This geometry includesthe intersection of the archwire plane with the tooth profile curve, theslot inclination angle and the slot in-out dimensions. In addition, thewire size and bracket geometry information are assembled, and tool sizeand clearance information are taken into account.

With this information, a bracket placement jig is designed for NCcontrolled manufacture to position the slot, and thereby the bracket,precisely on the tooth.

In FIG. 8D, a plastic jig 82 is shown which engages the walls and bottomof the bracket slot fully. Additionally, the portion of the jig 82contacting the tooth designed to be formed to precisely fit the knowncontour of the tooth, as determined by the profiles input in step (500).This assures that the bracket slot and hence the bracket is placed atprecisely the correct height when bonded to the tooth.

Brackets are placed so that the slots are not necessarily perpendicularto the long axis of the tooth but at varying degrees of cant. The jig 82accomplishes this goal by the use of an adapter 84 that fits into thebracket slot 82b and a coplanar slot 84a (FIG. 9T) to engage the plasticblade jig 82, as illustrated in FIG. 8D. The jig design substeps, whichare preferably performed in step (3500) and included in the detailedflowchart of the jig manufacturing step of FIG. 2Z, are summarized inthe flowchart of FIG. 2V. The design is converted into CNC code in step(3500) for controlling the jig forming machinery 41 primarily to cut acontoured surface that conforms the profiles of the tooth so that thejig fits in a precise position on the tooth to position the bracket foradhesion to the teeth,

In installation performed in the treatment operation (89), the jig 82 islined up with the long axis of the tooth crown when viewed from eitherthe front or facial surface of the tooth and from the biting or occlusalsurface. A plastic blade form of jig 82 offers visual reference to theheight of contour of the tooth and alignment of the bracket with themarginal ridges.

(97) Appliance Manufacturing Procedure:

The appliance manufacturing procedure (97), as illustrated in theflowchart of FIG. 2D, entails the generation of controller codes for NCmachinery to produce the brackets, archwires and bracket placement jigsdesigned in the appliance design procedure (96), and the manufacture ofthe appliance components with the use of the machinery controlled by thecodes. The procedure (97) includes the steps of:

(3000) Controlling and operating the bracket forming machinery 39 toproduce the custom brackets:

The bracket manufacturing procedure of the preferred embodiment involvesthe generation of NC code for the bracket slot cutting mill 39 of FIG. 1D, as illustrated in the flowchart of FIG. 2X. The step involves thegeometric relating of the tooth profile information PF for each tooth,and other tooth contour information of the shape of the surface of thetooth to which the bracket is to be attached from steps (300) and (400),and the archwire plane, slot inclination angle and slot depthinformation from steps (1200) through (1700). In addition, the bracketforming step performs the function of selecting the bracket blank fromwhich the bracket is to be fabricated. The bracket blank is made up of abase or pad that is attached to the tooth and an outwardly projectingsupport into which an archwire slot is formed.

The preferred embodiment includes the forming of brackets by cuttingcustom slots in bracket blanks while preserving the base inclinationangle. Brackets could be alternatively fabricated by inclining thebracket bases or pads. Additionally, bracket bases may be contoured toconform to the surfaces of the teeth, or a bonding agent may fill thespace between the bracket base and the tooth. Furthermore, while in thepreferred embodiments, a mechanical cutter blade forms the bracket,other means such as wire EDM, machining, casting or stereo lithographymay be employed.

(3200) Controlling and operating the Wire-bending machinery 40 toproduce the custom archwires:

The software that operates the computer 30c to drive the wire bendingapparatus 40 reads data files generated for the mandibular and maxillaryarchwires in steps (1600) and (1700) respectively. Also read by thecomputer 30c are data on the characteristics of the unformed wire 69,including that relating to the material of which the wire is made, aswell as its cross-sectional shape and dimension. The file that is readcontains coordinated data regarding calculated archwire segment lengthsand radii which cumulatively describes geometrically the desiredarchwire shapes. As explained above, the archwires consist of a sequenceof tangential arc segments with each segment a particular length andradius.

The arch forming software determines the position of the roller 70b ofthe anvil 70 that is required to produce a given radius in theparticular wire material and cross-section by going to a look-up table,previously derived and stored in a file accessible by the computer 30c,containing constants necessary to correct for each wire material andcross-section. The anvil 70 is driven to the desired position to producethe required radius and the feed roll motor 70c is driven to create thedesired length of wire at that radius. By adjusting the position of theanvil roller 70b and length of wire fed for with the roller 70b soadjusted, archwires 64 of the calculated final sequential tangentialradii are fabricated.

(3500) Controlling and operating the jig forming machinery 41 to makecustom placement jigs for the location of the brackets on the patient'steeth:

The machine control codes for controlling the jig forming machinery 41are produced directly from the tooth profiles generated in step 500 andfrom the archwire plane location of steps (1200) and (1400), the slotinclination steps (1300) and (1500), and the slot in-out dimensions fromthe steps (1600) and (1700). As stated above, the jig design step (1800)is preferably performed in the course of, and is described herein aspart of, the jig manufacturing step.

The profile data, which represents the profile curves with a fairly highresolution of data points is a series of straight line segments fordeveloping the codes for driving the NC equipment. Tool and bracketdimensions and design clearances are also taken into account, and CNCcodes are generated to cut jigs from circular plastic wafers on astandard CNC mill using a small carbide endmill tool. The details of thesubsteps of the step (3500) are included in the flowchart of FIG. 2Z.

(98) Appliance Transmission Procedure:

One of the ultimate objectives is to place the custom orthodonticappliance 25 into the hands of the orthodontist 14, along with the toolsand information necessary for the proper installation of the appliance25 in the mouth of the patient 12 to treat the patient by moving thepatient's teeth to the calculated finish positions. This is bestunderstood by reference to FIG. 1.

Referring to FIG. 1, as set forth above, the configuration of thepreferred system 10 will vary depending on the nature and scale of theorthodontist's practice. Preferably, all or much of the appliance designportion of the procedure (87) takes place at an appliance designfacility 13, although in a large scale orthodontic clinic, the entireprocess could be carried out at the patient treatment location. Usually,however, the functions performed in the design computer 30b, or designportion of the computer 30, are carried out at the appliance facility13, together with some of the manufacturing functions performed by themanufacturing control computer 30c and the appliance manufacturingequipment 38.

In the configuration where, as illustrated, some or all of the appliance25 is made at the appliance facility 13, the custom appliance 25 istransmitted to the orthodontist 14. Along with the appliance 25 iscommunicated documentation in the form of a hard copy printout ofinformation 37 generated by the design computer 30b, which could alsoinclude documentation of the input data that made up the data 26 and theprescription information 27, and a printout of parameters recorded bythe manufacturing computer 30c.

The transmitted appliance 25 includes a set of archwires 64, asillustrated in FIGS. 8E and 8F, a complete set of custom brackets 80, asillustrated in FIGS. 8D and 8F, and the placement jigs as illustrated inFIGS. 8D and 9T through 9W. Along with the jigs 82 are included a set ofadapters 84 that are used to align the slots 80b of the brackets 80 withcoplaner slots 84a of the jigs 82. The appliance and the bracketplacement jigs therefor are similar in the case of lingual appliances, abracket for which is illustrated on a tooth in FIG. 8G while the lingualappliance is shown positioned on the mandibular teeth in FIG. 8H.

In addition, custom archwires 64 are transmitted to the orthodontist 14.These archwires include archwires in the exact form, as illustrated inFIG. 8E, to move the teeth to their finish calculated positions, asillustrated, for example for the lower teeth, in FIG. 4D. In FIG. 4D,the archwire 64 is shown in the unstressed state (or having nominalresidual stress sometimes motivating some orthodontists to prescribeovercorrection) that it will attain when the appliance 25 has moved thepatient's teeth to the calculated finish positions. This is the sameshape as the archwire of FIG. 8E shipped to the orthodontist 14. Thisfinish archwire will be of a material and stiffness determined to beappropriate for the final positioning of the teeth. Depending on theseverity of the initial malpositioning of the patient's teeth, however,less stiff archwires, or temporary archwires may be desired forbeginning the orthodontic treatment. Thus, additional archwires 64 ofvarious properties but in the shape shown in FIG. 8E will be providedthe orthodontist 14. In addition or in the alternative to the provisionof these additional archwires, an actual size drawing or template havingthereon the shape shown in FIG. 8E will be provided the orthodontist 14to enable him to form archwires for preliminary treatment and roughpositioning.

In alternative configurations, information may be sent from the designcomputer 30b in machine readable form, for example by diskette 34 ormodem, to a manufacturing computer 30c to which is attached one or moreof the appliance component manufacturing machines 38.

(89) Patient Treatment Operation

The patient treatment involves, first, the assembly of the respectivebracket 80, jig 82 and adapter 84 combinations, as illustrated in FIG.8D, and the application of the brackets 80 thereby to the patient'steeth. This involves the application of adhesive to the area generallyin the center of the face of the tooth, either labial or lingual, towhich the brackets 80 are to be applied. This is illustrated in FIG. 8D,for example, with the application of a bracket 80 to the labial face ofa maxillary incisor T_(U),1. The assembly is positioned on the toothwith the blade of the jig 82 positioned on a generally vertical labiallingual cross section through the approximate center of the tooth, inthe plane that may be said to contain the crown long axis CLA of thetooth.

When the bracket adhesive has set, the bracket placement jig 82 isremoved by first sliding out the adapter 84 mesiodistally and thensliding the jig 82 off of the incisal edge of the tooth, leaving thebracket in the calculated position.

Then, with the brackets 80 set on the teeth the archwire 64 isinstalled. Often, the first archwire installed will be one of lowerstiffness than the final archwire. In the example of FIG. 8F, themandibular teeth in their initial position as illustrated in FIGS. 4 and4A are shown. The brackets 80 are positioned on the teeth in the exactsame positions as shown in the calculated finish position diagram ofFIG. 4D. Because the teeth are not yet in this ideal finish position,the archwire 64, when inserted into the archwire slots and tied to thebrackets 80, will be stressed into the elastically deformed conditionshown in FIG. 8F. This stressed condition of the archwire 64 operates,without the need of the orthodontist to artfully bend the wire, to applythe forces to the teeth to urge them toward the ideal positions of FIG.4D. This force will continue to be applied until the teeth have moved tothe finish positions. In some prescribed forms of treatment, the wireand brackets are designed to move the teeth to a slightly overcorrectedposition to allow for a relaxation movement of the teeth when theappliance 25 is removed.

DETAILS OF STEPS OF APPLIANCE ANALYSIS, TOOTH POSITION CALCULATION, ANDAPPLIANCE DESIGN AND MANUFACTURING OPERATION (87)

The analysis, design and manufacturing operation (87), as stated above,includes the (94) input, (95) analysis, (96) design, (97) manufacturing,and (98) transmission procedures of a computerized custom designedappliance manufacturing operation. The steps of those procedures, asoutlined above, include the following:

Digitized Input Procedure (94)

The input of digitized information includes the (100) input of patientand doctor identifying information, (200) the input of patientbackground information, (300) the input of digitized information of thehorizontal dimensions of the mandibular teeth and the mandibular bone,(400) the input of horizontal dimensions of the maxillary teeth, and(500) the input of vertical labial-lingual profile information of eachof the individual teeth.

(100) Identification Information Input step:

The first step in the procedure (82), as illustrated in flowchart ofFIG. 2A, is (100) to input the doctor-patient identification information17. This step (100), as illustrated in the detailed flowchart of FIG.2E, includes the substeps, performed by an operator 28 in response toprompts for text input at a terminal of the computer 30, of (105) inputof the doctor's name, (110) input of the doctor's identification number,and (115) input of the patient's name. Then, the computer 30 (120)assigns a patient identification number. With this information, (125) apatient-specific floppy disk or diskette 34 is automatically formatted.

(200) Patient Background Input Step:

The next step in the information input procedure (94), as illustrated inFIG. 2A, is (200) the entry, in response to prompts, of the patientbackground information 19, and the prescribed treatment information 27from the doctor. This step, as illustrated in the detailed flowchart ofFIG. 2F, involves the substeps of (205) entering, from the backgroundinformation 19, the patient's age as numerical data, and selecting (210)the patient's sex and (215) the patient's race from options on thescreen. Then, from the prescription information 27, the data areentered, by selecting choices from multiple choice prompts, frominformation such as the following:

(220) Whether or not the treatment is to include an extraction, and ifso, which teeth are to be extracted;

(225) Whether the occlusion type is a group function or a cuspid rise,and if a cuspid rise, whether averages or individual head film is to beused;

(230) Whether the prescribed procedure is to preserve lower intercuspiddistance or allow expansion, and if expansion is to be allowed, how muchexpansion;

(235) Whether or not the occlusion is mutilated;

(240) Whether a Steiner compromise is to be allowed to accommodateskeletal discrepancy;

(245) Whether a Roth or Ricketts inset is to be used on upper laterals,and if so which;

(250) Whether a Roth or Andrews upper lateral overbite is indicated, andif so, which;

(255) Which is the preferred slot size, from traditional sizes 0.018" or0.022" (0.45 mm or 0.55 mm), or other available size, of which 0.20"(0.50 mm) would often be acceptable;

(260) Whether the case is to be treated with labial or lingualappliances;

(265) Whether the case is to be diagnosed using symmetry or not;

(270) How inter-incisal angle is to be determined, using the AndrewsNorms, the Parallel Upper Central to Facial Axis Norm, or Ricketts Norm.

(300) Mandible Digitized Video Input Step:

The forming of the computerized mathematical model of the teeth of thepatient 12 begins with (300) the inputing of video or other graphics topview image of the patient's lower jaw, including the teeth, asillustrated in the detailed flowchart of FIG. 2G. Such an image as inputby the video scanner 43, is illustrated in FIG. 3.

The step (300) includes the digitizing and processing of the data of thewidths of the mandibular teeth and size and shape of the mandibular boneor bone of the lower jaw 22 of the patient 12 from the horizontal planview of the lower jaw as in FIG. 4. The mandible 22 is composed of hardor cortical bone on the external surface and soft or cancellous bone inthe interior. This bone is not as orthodontically alterable as is themaxilla. Since the lower teeth must remain in the mandible,determination of its shape and boundaries is made so that a skeletalarch can be defined to be used as a starting point in the calculation ofthe finish position of the teeth.

The lower teeth must lie on the mandible 22 in an arch that may bedefined as the mandibular trough MT, as illustrated in FIG. 4. The rootsof the lower teeth of the patient are contained within the mandibulartrough MT, which is defined as the space between boundaries B_(L) andB_(B) of FIG. 4. The outer, or buccal, and inner, or lingual, boundariesB_(B) and B_(L), respectively, are preferably digitized by interactiveselection by the operator 28 from an image 48 of the cortical bone ofthe mandible 22 on the screen 35. Furthermore, the mandibular teeth mustlie in the arch in contact with one another. They each occupy a portionof the arch equal to the distances between their mesial and distalcontact points with the adjacent teeth. These tooth extremities are alsopreferably digitized by interactive selection from the image 48.

To (300) input data of the patient's mandibular teeth and lower jaw 22,as illustrated in the detail flow chart of FIG. 2G, (305) a videographics image 48 (FIG. 3) of mandibular model 21 is first input to thescreen 35 of the computer 30c. Then (310) a grid G is overlaid on thevideo image of the mandibular 22 as illustrated in FIG. 4. The grid G ispresents grid lines that intersect the image 48 on the screen, Theoperator 28 (315) resizes the grid G, if necessary, and orients theimage relative to grid G to define X, Y coordinates with a Y axis on amidline ML of the lower jaw 22 and an X axis perpendicular to the Y axisthrough a selected intersection point or origin O,O, preferably set atthe mesial contact points of the lower central incisors.

Next, the computer 30 prompts the operator sequentially to select eachpoint, first for the individual tooth contact points, then the jaw boneboundaries. With the pointing device 47, (320) the operator 28 moves thecursor on the screen 35 and selects (e.g., clicks with a mouse on) theprompted point, thereby initiating the software for digitizing the X,Ycartesian coordinates of the mesial and distal extremities M_(X),Y andD_(X),Y, respectively, for each mandibular tooth. The mesial extremityM_(X),Y of a tooth is the point on its surface closest the midline MLalong the mandibular arch (the mesial direction m) while distalextremity of a tooth is the point on its surface closest the rear of themouth along the mandibular arch (the distal direction d). From the X, Ycoordinates of M_(X),Y, M_(X) and M_(Y), and of D_(X),Y, D_(X) andD_(Y), (325) the mesio-distal width MDW_(I) of each tooth I, on eachside of the mandible 22, is calculated using Pythagorean theorem:##EQU1## where: M_(X) is mandibular X coordinate.

M_(Y) is mandibular Y coordinate.

D_(X) is distal X coordinate.

D_(Y) is distal Y coordinate.

These widths are then summed to calculate the total length MAL requiredof the arch to accommodate the mandibular teeth. Since all of the teethwill be finally positioned to be in contact with the adjacent teeth,this length remains a constant length of any arch on which themandibular teeth are placed in the calculations.

Then, by moving the pointing device 47 to the intersections of the linesof the grid G with the visible boundaries B_(B) and B_(L) and selectingthe intersection points, data is input for determination of the shape ofthe mandibular trough MT. The point selection function can be made withconventional available CAD/CAM, imaging or illustration software and thepointing device 47. (330) From the selected intersections of the linesof the grid G with the mandible boundaries B_(B) and B_(L), cartesiancoordinates La_(X),Y and Li_(X),Y of labial and lingual limits,respectively, of cortical bone on both sides of mandibular jaw aregenerated. The X, Y coordinates La and Li so chosen are digitized asabove on the boundary lines B_(L) and B_(B) of the cortical bone,between and interproximate the teeth.

After the points La and Li are chosen representing the cortical bonelimits, (335) midpoint coordinates MP_(XY) are calculated between eachof the individual labio-lingual pairs of La and Li. Also, calculated arethe bone width distances between each of the respective labio-lingualpair DLL, as follows: ##EQU2## where: La_(X) is labial X coordinate ofpoint La,

La_(Y) is labial Y coordinate of point La.

Li_(X) is lingual X coordinate of point Li.

Li_(Y) is lingual Y coordinate of point Li.

These midpoints MP_(X),Y, one of which is the designated originMP_(O),O, lie on an arch that describes the size and shape of the centerof the cancellous portion of the mandibular bone 22.

At this point, the beginning of the analysis for the calculation of thefinish positions of the teeth is carried out. The coordinates of pointsMP_(X),Y are recalculated relative to a new origin O,O at the calculatedmidpoint between the mandibular centrals, to normalize the mandibulartrough equation to its own independent midpoint when calculated below.The sum of the individual mandibular tooth widths MDW equals the totaldental length or mandibular arch length MAL contained in the mandibulartrough equation MTE that will be constructed through the pointsMP_(X),Y. MAL is referred to as the arch perimeter.

At this stage, (340) the midpoints are typically averaged right to leftto eliminate any asymmetry that may be present due to slight measurementerrors. If, however, the patient has been diagnosed by the orthodontist14 to be of asymmetrical anatomy, the averaging process is notperformed. Such a determination will have been made by the orthodontist14 in the examination procedure (90) described above and specified ofthe prescription 27 in step (265) of the procedure (92) described above.An advantage of the averaging process is that, when used, it assists thefinal positioning of the teeth symmetrically about the midline ML andwill make it easier for an archwire to be produced that is symmetricalfrom right to left, and thus can be made such that it can be installedin inverted orientation.

The midline ML shown in FIG. 4 is the axis of such symmetry corrections.These corrections for each point MP_(X),Y are calculated as follows:##EQU3## where: S_(X),Y is the symmetricalized point MP_(X),Y

MP_(X),Y is mid-point of mandibular trough

PR_(X),Y is a point MP_(X),Y on the right side

PL_(X),Y is the corresponding point on left side of the trough

With the completion of this symmetricali-zation process, a mathematicalequation MTE, which describes the size and shape of the mandibulartrough according to steps (345), (350) and (355), is derived by fittinga curve to the points MP_(X),Y. Preferably, this curve is derived byfitting a series of cubic equations, such as a cubic spline equation, topass smoothly through the points, for example, through the averagedmidpoints S_(X),Y. The cubic equations allow the determination of theslope of the curve at each of the midpoints.

The cubic equations are then preferably converted in form to a series ofsegments of tangent circle equations with slopes equal to the slopes ofthe cubic spline at the midpoints, and equal to the slopes of theadjacent circle segments at the segment end points, or their points ofintersection, along the curve. To fit a cubic equation with quadratics,two circles CS and CL are used to describe each segment of the MTEbetween midpoints, as illustrated in FIG. 5. This allows a smooth curveconsisting of tangential circles to represent the mandibular trough.

The cubic equation calculations are preferably those performed by (345)calculating cubic spline parameters required to pass a smooth curvesthrough symmetricalized midpoints S_(X),Y as illustrated in FIG. 5A.This includes (350) calculating the slope of the cubic spline curve ateach symmetricalized mid-point S_(X),Y or S_(X),Y, and (355) calculatinga series of tangential circle equations whose slopes are equal at themid-points and at points of intersection along the curve.

(345) The cubic spline method preferred uses a cubic, or third degree,polynomial to interpolate between each pair of data points S_(X),Y. Adifferent polynomial is used for each interval, and each one isconstrained to pass through the original data with the same slope as thedata. (350) The slopes of the cubic equation are computed by solving theslope of a parabola that passes through each data point and its twonearest neighbors points. The cubic spline method is described in moredetail in the discussion of the cubic spline subroutine (2000) below.

(355) Any point on the cubic spline equation can now be calculated byusing a cubic spline interpolation. Using this, the cubic splineequation is subjected to a circle segment conversion by which the formof the equation MTE is converted to a series of circle segments thatinterconnect tangentially. Once the spline equation is derived, theslopes at each data point are calculated using the point slope method.These slopes are utilized to derive, between each pair of data points onthe spline equation, the description of two circle segments, each fromone of two circles as illustrated in FIG. 5, to convert the MTE to aseries of circle segments throughout its length. This facilitates thesetup of the teeth, the description of the configuration of archwires,and the generation of NC code for the manufacture of the appliance. Thespline-to-circle conversion routine is described in further detail underroutine (2100) below.

The input procedure continues. (360) Cartesian coordinates are input forright and left mandibular cuspid cusp tips CR and CL, respectively, asillustrated in FIG. 4. (365) A distance DCT between the cusp tips CR andCL of the two mandibular cuspids is then calculated: ##EQU4## where:CR_(X) =right cuspid X coordinate.

CR_(Y) =right cuspid Y coordinate.

CL_(X) =left cuspid X coordinate.

CL_(Y) =left cuspid Y coordinate.

This information is used to calculate if and how much the mandibularintercuspid distance is to be altered, and to evaluate whether thecalculated final position is acceptable. Similarly, (370) cartesiancoordinates or right and left mesio-buccal cusp tips, MR and ML,respectively, of mandibular first molars are calculated, and (375) thedistance between these points DMT is calculated: ##EQU5## where: MR_(X)=right first molar cusp X coordinate.

MR_(Y) =right first molar cusp Y coordinate.

ML_(X) =left first molar cusp X coordinate.

ML_(Y) =left first molar cusp Y coordinate.

This information is used to determine if and how much the mandibularintermolar distance is to be altered.

(400) Maxilla Digitized Video Input Step:

As with the mandibular jaw information described in connection with FIG.4, (400) a computer image is made from input in the same manner from theupper model 23 of the maxillary jaw 24 of the patient 12, as illustratedin the flowchart detail of FIG. 2H. This involves the substeps of (405)inputing a video image 48a of maxillary model 23 to the computer screen35. The image 48a is illustrated in FIG. 4A. With the maxilla, it is notnecessary to overlay the grid G on maxillary image on the screen, sincethe bone of the maxilla is a variable that will be alteredorthodontically to accommodate the finish positions of the teeth. Theorientation of the axes and position of the origin are immaterial to thecalculation of the relative distances such as MDW of the teeth. Only thescale must be maintained. As with the mandibular information, the imageof the maxillary jaw 24 is displayed at a scale predetermined by thescanner 33. The scale is involved in the calculation of the maxillarytooth widths MDW.

(420) Cartesian coordinates of mesial and distal extremities M_(x),y andD_(x),y of each maxillary tooth are then input as with the mandibularteeth and (425) the mesio-distal width MDW of each maxillary tooth iscalculated using Pythagorean theorem, thus: ##EQU6## where: M_(X) ismesial X coordinate.

M_(Y) is mesial Y coordinate.

D_(X) is distal X coordinate.

D_(Y) is distal Y coordinate.

This information is used first to determine whether the maxillary andmandibular teeth are correct in proportion to the mesiodistal widths MDWof the other. If the proportions are incorrect, a tooth size discrepancyTDS is said to exist, and the information is recorded to report to theorthodontist. The MDW's of the maxillary teeth are later used to placethe maxillary teeth upon the mandibular arch.

Next, (430) coordinates of the central fossae of right and leftmaxillary first molars are input. Then, (435) the distance betweencentral fossae DCF is calculated as follows: ##EQU7## where: R_(X) isright side central fossa X coordinate.

R_(Y) is right side central fossa Y coordinate.

L_(X) is left side central fossa X coordinate.

L_(Y) is left side central fossa Y coordinate.

This information is recalculated after the tooth finish positions arecalculated to coincide with the DMT spacing of the mandibular firstmolars, and compared with this initial measurement as an indicator ofwhether the intermolar width will be changed by treatment and the amountof such change, if any.

(500) Digitized Probe Tooth Profile Input Step:

The next input step (500) involves an analysis of the dentition, asillustrated in the detailed flowchart of FIG. 2I. In this step, selectedprofiles of each of the teeth are generated from either the model 20, orfrom a digitized three dimensional representation of the patient's teethor the model 20 as illustrated in FIGS. 3A and 3B. In the illustratedembodiment, the use of the probe assembly 57 of FIG. 1C is used in thisstep.

Where the full three dimensional scan has been employed in step (300),as could be produced with the use of the laser image generator (FIG.1B), or as could be produced with moire image generator or othertechnique, a digitized computer model is produced. From such a computermodel, which is an electronic version of the model 20 in the formillustrated in FIGS. 3A and 3B, planes or other cross-sections throughthe teeth are selected that contain extremities of the teeth. The threedimensional images may be displayed on the screen 35 and profilesgenerated either with the pointing device 47 in a manner similar to theuse of the mechanical probe described below, or automatically usingavailable CAD or illustration imaging software. Whether the profiles aregenerated from a physical model 20 or an electronic version thereof,much of the input step (500) and/or the landmark selection step (600)may be similarly employed.

In the preferred use of the information from the probe assembly 57, asingle digitized profile curve PF is constructed for each tooth in agenerally vertical plane extending in an approximately labial-lingualorientation generally along the central developmental lobe perpendicularto the marginal ridges. While other profiles can be taken, the need todo so is reduced by intelligent plane selection made with anunderstanding of tooth anatomy, depending on the data required by thetooth positioning and appliance design criteria employed. The selectionof the profile plane is illustrated in FIG. 6 where a first profilePF_(A) through the center of the tooth is shown as missing the buccalcusp tip which is the maximum crown highpoint of the tooth. ProfilePB_(B) is then selected to include the buccal cusp, and the ridge of theprofile is found to generally align with the lowpoint of PF_(A).Alternatively, the profile may be non-planar to pick the importantfeatures of both planes. As such, the profile produced will becomparable to a projection onto a plane of the relevant toothextremities.

The step (500) of analysis of the dentition includes, first (505)examination, by the operator 28 of the computer 30a, of the marginalridges of the upper central and upper lateral teeth. If ridges areexcessive, a determination is made to take a profile twice with theprobe 60, once by smoothing the teeth, for example with wax, for archcoordination and once without smoothing for placement jig geometry.Otherwise, a single profile taken across the buccal cusp will containinformation of the crown height of the tooth as well as approximatingthe profile of the tooth through its mesiodistal center with accuracythat is usually sufficient. Then, (510) a determination is made as towhether one or two traces of maxillary incisor teeth are to be input asin step (505) above.

(515) The computer 30a is configured to receive sequential cartesiancoordinate pairs through an RS-232C serial port representing toothprofile anatomy from the orthogonally positioned displacementtransducers 61. (520) The computer 30a prompts the operator 28 to enterthe profiles of each tooth sequentially. In response to the prompts,data points of each tooth are input, beginning with lower left molarT(B,L,6) and ending with upper right molar T(U,R,6), and a display 63 ofprofile PF_(I) image is generated. The output circuits associated withthe transducers 61 are configured to digitize data values at periodictime intervals as the probe 60 is moved across the teeth from the timethe probe first starts to move across the tooth until the operatorenters a command or key stroke indicating that the scan is complete.Then (525) the input profile data of each of the teeth is stored inmemory by the computer 30. The resulting profiles PF_(I) are illustratedin FIG. 3C. These profiles, at this stage, are not related to thepositions of the teeth within the mouth or with respect to other teeth.Thus, each of the X-Y coordinates of the individual tooth profiles areindependent of each other. In step (600) below, the coordinate axes ofeach tooth will be oriented with respect to each other, and thereafter,in later steps (800)-(1100), the coordinates of each profile aretranslated vertically for proper occlusion and horizontally forplacement on their respective arches.

(95) Analysis and Finish Tooth Position Calculation Procedure

The calculation of the finish positions of the teeth, as illustrated inthe flowchart of FIG. 2B, includes (600) determining the relativepositions of geometric landmarks on the surfaces of the teeth andestablishing the axis inclinations of the teeth, (700) calculatingcuspid rise, (800) initially positioning the mandibular teeth verticallyand in relation to the mandibular trough, (900) calculating a best fitcusp tip equation for the mandibular teeth, (1000) calculating thefinish positions of the mandibular teeth on the best fit equation, and(1100) calculating the finish positions of the maxillary teeth on threearches related to the best fit equation.

(600) Tooth Landmark Identification Analysis Step:

After the individual teeth have been digitized, the inputing of toothshape data (94) is complete, with the digitized information 26 stored afile. Then, referring again to the flowchart of FIG. 2, (95) the inputdata 26 is analyzed to develop or derive further parameters forcalculating the final positions of the teeth and for (96) the design ofthe appliance 25. In the tooth positioning analysis (95), as illustratedin the flowchart of FIG. 2B, (600) a tooth profile analysis is made inwhich, for example, certain anatomical landmarks are chosen, dependingon the tooth to be analyzed. The details of the tooth profile analysisare illustrated in the flowchart of FIG. 2J.

In the tooth profile analysis step, (605) individual images 63 of theprofile curves PF_(I) of each tooth (FIG. 3C) are recalled separately tothe screen of the computer 30b for selection of the landmarks.

Using the displayed images 63 of the profile curves PF_(I), (610)specific landmark points are chosen, first on the mandibular molars andbicuspids. The selected points are digitized as illustrated in FIG. 6.The selected points are:

Point P₁ : The Lingual (tongue side) gum/tooth intersection.

Point P₂ : The prominence of the lingual cusp.

Point P₃ : The prominence of the buccal (cheek side) cusp.

Point P₄ : The buccal gum/tooth intersection.

From these landmarks, (615) the crown long axis CLA of each molar andbicuspid profiled is determined. The determination is made byconstructing a first line L₁ between points P₂ and P₃ and a second lineL₂ between points P₁ and P₄. The crown long axis CLA of a tooth is theline between the midpoints of L₁ and L₂.

Line L₁ is constructed through point P₂ and point P₃ by the followingequation: ##EQU8## where: X₂, Y₂ =X and Y coordinates of point P₂.

X₃, Y₃ =X and Y coordinates of point P₃.

Line L₂ is constructed through point P₁ and point P₄ by the followingequation: ##EQU9## where: X₁, Y₁ =X and Y coordinates of point P₁.

X₄, Y₄ =X and Y coordinates of point P₄.

A point equidistant between points P₂ and P₃ along line L₁ is thencalculated and defined as P₂₋₃ : ##EQU10## where: X₂, Y₂ =X and Ycoordinates of point P₂.

X₃, Y₃ =X and Y coordinates of point P₃.

A point equidistant between points P₁ and P₄ along line L₂ is alsocalculated and defined as the Gingival Center Point GCP: ##EQU11##where: X₁, Y₁ =X and Y coordinates of point P₁.

X₄, Y₄ =X and Y coordinates of point P₄.

The line defining the crown long axis CLA is constructed using thefollowing equation:

where: ##EQU12## X₂₋₃, Y₂₋₃ =X and Y coordinates of the center pointP₂₋₃. X_(GCP), Y_(GCP) =X and Y coordinates of gingival center pointGCP_(X),Y.

For molars and bicuspids, point P₃, the buccal cusp tip, is defined asthe Incisal Center Point ICP.

Similarly, (610) the anatomical landmarks and crown long axis CLA forthe mandibular cuspids, laterals and central teeth are determined, asillustrated in FIG. 6B. The points P₁ through P₄, as labeled in FIG. 6B,are selected as follows:

Point P₁ : The lingual gum/tooth intersection.

Point P₂ : The lingual aspect of the incisal edge.

Point P₃ : The buccal aspect of the incisal edge.

Point P₄ : The facial gum/tooth intersection.

As with the bicuspids and molars, lines L₁ and L₂ are constructed. Thelandmarks in the cases of the teeth as illustrated in FIG. 6B, arechosen because they are relatively tolerant to operator error inselection. This can be seen by the set of broken lines that are possiblealternatives to L₂ in FIG. 6B. From these landmarks (615) the crown longaxis CLA is determined as defined above, by connection of the midpointsof L₁ and L₂.

The next step in the analysis is the determination of maxillarydentition for each upper molar and bicuspid. (610) Anatomical landmarksare identified and chosen as illustrated in FIG. 6C, which requires(612) the selection of a fifth point, P₅, defined as follows:

Point P₁ : The lingual gum/tooth intersection.

Point P₂ : The prominence of the lingual cusp.

Point P₃ : The prominence of the buccal cusp.

Point P₄ : The buccal gum/tooth intersection.

Point P₅ : The mesial marginal ridge of the tooth at central groove.

Referring to FIG. 6C, from the landmarks, (615) the crown long axis CLAof each applicable maxillary tooth is determined.

The (610) anatomical landmarks for the maxillary cuspids, laterals andcentral teeth are determined as illustrated in FIG. 6D. The pointslabeled P₁ through P₄ are selected, as follows as illustrated in FIG.6D:

Point P₁ : The lingual gum/tooth intersection.

Point P₂ : The lingual aspect of the incisal edge.

Point P₃ : The buccal aspect of the incisal edge.

Point P₄ : The facial gum/tooth intersection.

From each of these sets of landmarks, the crown long axis CLA of eachsuch tooth is also determined as described (615) above.

This completes the loop (620) for all of the teeth.

Next, as further illustrated in FIG. 6D, (620) seed values for settingthe crown long axis inclinations LAI of the teeth. Initially, such seedvalues may be derived from analyses that identified the facial axisplane FAP through the facial axis point FA of the tooth (the midpointsof the height of the clinical crowns along the facial axes of theclinical crowns) as described by Dr. Lawrence Andrews. It is, however,contemplated that CLA seed values for various population groups will bestatistically derived in the course of the practice of the presentinvention, and will produce improved treatment results.

The seed values shown in Table 1 below are typical for caucasian males.These seed values for tooth LAI, tabulated in degrees from thehorizontal lingual (-X) axis, will vary to reflect known variations dueto such things as sex,

The preferred seed values are shown in Table 1 below are typical forcaucasian males. These seed values will vary to reflect known variationsdue to such things as sex, race or treatment plan.

                  TABLE 1                                                         ______________________________________                                        Tooth          Maxillary Mandibular                                           Type           Crown LAI Crown LAI                                            ______________________________________                                        Central        117       107                                                  Lateral        112       107                                                  Cuspid         108       100                                                  1.sup.st Bicuspid                                                                            94        83                                                   2.sup.nd Bicuspid                                                                            94        80                                                   1.sup.st Molar x         x                                                    2.sup.nd Molar x         x                                                    ______________________________________                                    

The computer images as summarized in FIG. 3C for each tooth (630) arethen rotated so that the CLA is oriented at the angle LAI, the long axisinclination angle, to the mandibular trough plane MT according to thevalues in Table 1. This computes the final inclinations of the teeththat will be preserved in the calculations below. This produces theoriented profiles PF summarized in FIG. 6E.

In the analyses of Andrews referred to above, the LAIs were establishedwith a line L_(FA) drawn tangent to the facial surface at FA, and linerepresenting the relative inclination of the archwire plane drawnthrough FA point. The angle between the lines was established at theinclinations reported by Andrews for patients with no skeletaldiscrepancies. The angle LAI between the crown long axis CLA and a linerepresenting the maxillary arch plane in which lies the mandibulartrough equation MTE is related to the facial inclination angles ofAndrews' studies by taking into account statistically the thicknessesand contours of the teeth. Table 1 above was derived, after statisticalprocessing, to produce the seed value used for the final inclination ofthe crown long axis in preferred occlusal design.

Once the tooth profiles have been rotated to the inclination angles LAI,certain precise vertical dimensions and extremities can be determined.From the digitized profile curves, which are stored in memory in theform of a series of closely spaced points, the precise incisal tip IC,as illustrated in FIGS. 6F, 6H and 6I, are identified on the cuspids,laterals and centrals.

Additionally the elevation of the marginal ridge P₅ is identified. Themarginal ridge elevation MRE, which is the vertical distance from P₃ toP₅, is identified on the maxillary posterior teeth because they are thecentric stops for the buccal cusps of the mandibular molars andbicuspids. In other words, point P₃ on the mandibular molars andbicuspids contacts point P₅ on the maxillary molars and bicuspids whenthe teeth are together, as illustrated in phantomline PH₁, in FIG. 6C.For a more precise placement in a less common case where the maxillaryridge is narrow in relation to the mandibular tip (phantom line PH₂), amore detailed three dimensional analysis of the tooth shape can takeinto account additional correction needed. The calculation of MRE (FIG.6C) is made after rotation of the teeth to their proper LAI inclinationsso that MRE will be a vertical distance, where LAI is measured relativeto the plane of the dental arch. The MRE is used as the buccal cuspheight BCH in the calculation of cuspid rise and archwire planeplacement as described below in the discussion of FIGS. 7A and 8, 471respectively.

(700) Cuspid Rise Determination Step:

The next step of the analysis procedure (87) is (700) the calculation ofcuspid rise, illustrated in detail in the flowchart of FIG. 2K.

Most orthodontists currently desire a cuspid rise occlusion, in which,in lateral movement of the lower jaw, the cuspids cause the other teethto disclude or to come apart. In order for this to happen, the overlapof the cuspids must be greater than that of the other teeth when theteeth are together. This is complicated by the fact that the cuspids(I=3) are close to the front of the mouth and are therefore further fromthe condyle or pivot point PP of the jaw than are the posterior teeth(I>3), as illustrated by distances DJ_(I) in FIG. 7. This results in theteeth closer to the back of the mouth moving less than the cuspids onopening. This differential rate of movement must be included in thecalculation of cuspid rise or the back teeth will remain in contactafter the cuspids have cleared each other. Also, the distance DPP fromthe occlusal plane to the pivot point PP of the condyle of the jaws mustbe considered, as illustrated in FIG. 7. A failure to provide for thisdistance results in what is known as working interferences.

According to the preferred embodiment of the present invention, wherecuspid rise is prescribed to control occlusion, the contribution ofcuspid rise is distributed between the maxillary and mandibular cuspids,with two parts of the cuspid rise provided by the maxillary cuspids andone part by the mandibular cuspids. This distribution is applicablewhere occlusion is solely to be a cuspid rise function, Where occlusionis to be a group function, as specified by the orthodontist 14 in theprescription 27, the distribution between the upper and lower teeth isgenerally equal.

In the substeps performed in the calculation of the cuspid rise (700),illustrated in detail in the flowchart of FIG. 2K, the first substep is(705) to acquire the initial vertical distance or buccal cusp height BCHfrom P₃ to the marginal ridge for each of the right and left maxillaryfirst bicuspids T(U,4), second bicuspids T(U,5), first molars T(U,6),and second molars T(U,7), as illustrated in FIG. 6C. This is themarginal ridge elevation MRE calculated for each of these teeth insubstep (615) of step (600). Then, from anatomical study, (710) the uesin Table 2.

    1.67×BCH of T(U,7)

    1.50×BCH of T(U,6)

    1.36×BCH of T(U,5)

and

    1.20×BCH of T(U,4).

TABLE 2

Then, (715) from the products of the buccal cuspcuspid rise verticalheight CR required to clear each respective pair of teeth is determinedby first computing the values in Table 2, which are derived from the jawdimensions DPP and DJ_(I) in FIG. 7. required to clear each respectivepair of teeth is determined by first computing the val height BCH foreach such tooth multiplied by the rise factor listed above, the largestvalue is selected. This selected product is the cuspid rise required toclear the most prominent cusp and provide group function occlusion. Thisis illustrated as BCH₆ in FIG. 7A for the case where the first molarsare the last to clear.

(720) If the group function has been selected in the prescription 27provided by the orthodontist 14, the calculated rise is used as is. Ifcuspid guidance has been selected in the prescription 27 of theorthodontist 14, the calculated cuspid rise factor must further bemodified to give typically 0.5 to 0.75 mm of clearance over the largestrise factor by multiplying the buccal cusp height BCH for each tooth bythe rise factor listed above and selecting the largest figure, thenadding 0.5 to 0.75 mm additional cuspid overlap to obtain and adjustedcuspid guidance cuspid rise.

(725) Calculation of cuspid overlap or cuspid rise CR for maxillary andmandibular cuspids is preferably as follows: If group function has beenselected, mandibular rise equals 50% total group function rise, andmaxillary rise equals 50% of the total group function rise. If cuspidfunction has been selected, mandibular rise equals 34% of the totalcuspid guidance rise, and maxillary rise equals 66% of the total cuspidguidance rise.

(800) Mandibular Tooth Placement Step:

The next step in the analysis procedure (87) is (800) the mathematicalconstruction of the mandibular occlusion to calculate the position ofthe mandibular teeth. The details of this step are illustrated in theflowchart of FIG. 2L. The first calculation places the tips of themandibular teeth on an occlusal plane pending final refinement of theplacement, as diagrammatically illustrated in FIG. 6E. In this step, theinclinations of the mandibular tooth crown long axes CLA are preserved,and the teeth are moved upward along their CLA's until their tips are inalignment with the plane of the top of the tallest tooth. The CLA's areplaced to intersect the MTE below the tooth GCP. Because the teeth areinclined at different LAIs, or long axis inclination angles, the toothtips will each be differently offset from the MTE, and thus not in asmooth arch.

The substeps of the mandibular placement step (800), illustrated in theflowchart of FIG. 2L, are as follows:

(805) The tallest mandibular tooth, with the exception of the cuspids,is identified. In FIG. 6F this is illustrated as the left mandibularcentral. The tallest tooth is the tooth with the greatest crown heightCH. The crown height CH is the distance, in the Y direction (with theteeth profiles oriented as described in step (600), from the GCP, thepoint of intersection of line and crown long axis CLA, to highest pointon buccal cusp, e.g. P₃ (for posterior teeth) as illustrated in FIG. 6Fand (for the anterior teeth) to either the incisal center point ICP or,preferably to the incisal tip IC, as illustrated in FIG. 6G. The crownheight CH of the tallest tooth, shown as the left mandibular centralincisor in FIG. 6F, is the maximum crown height MCH of the mandibularteeth.

Then, (810) three parallel planes are established:

a) an MCH reference plane MCHP parallel to the X-axis, and passingthrough an origin O,O, set at the GCP of the tallest tooth (FIGS. 6F and6I);

b) a Buccal Cusp Plane BCP parallel to X-axis and passing throughcoordinates O, MCH on the tallest tooth (FIGS. 6F and 6I); and

c) a Cuspid Rise Plane CRP parallel to X-axis and passing throughcoordinates O, where CR is the cuspid rise calculated in step (700),where the cuspid rise option has been selected.

With the planes defined, (815) the oriented mandibular teeth are placedsuch that the highest point on buccal cusp tip P₃ or incisal tip IC ofeach contacts the buccal cusp plane BCP, for all teeth except thecuspids, as illustrated further in FIG. 6F. The BCP thereby isestablished as the occlusal plane MOC. The reference plane MCHP is setequal to the plane of the mandibular trough MT. This sets the GCP of thetallest tooth on the MT, with the GCP's of the remaining mandibularteeth above it. It also sets the occlusal plane MOC a distance MCH fromthe mandibular trough MT. The absolute highest point on a tooth crown ispreferably used to align the teeth with the BCP. Such a point can bedetermined by additional point selection in step (500), such as by thedirect selecting of the point IC for the precise incisal tip, orpreferably by calculating the highest point directly from the profilesof FIG. 3C or from three dimensional images as in FIGS. 2A, 2B afterrotation of the teeth to their final inclination angles LAI, at the endof step (600).

The next stage in this step is to establish the mandibular component ofcuspid rise. This involves (820) vertically moving the cuspids by, forexample, sliding the cuspids along their crown long axes, such that thecuspid cusp tips are at the appropriate height above the mandibularocclusal plane, that is, in the plane CRP.

At this stage, the vertical positions of the mandibular teeth relativeto each other are calculated, providing a basis for relating the Ycoordinates of the individual mandibular tooth profiles with respect toeach other as illustrated in FIGS. 6F and 7C.

Then, with the mandibular teeth vertically positioned, the teeth arehorizontally set at temporary positions with respect to the MTE, whichlies in the plane of the mandibular trough MT (MCHP). This horizontalpositioning, in effect, relates the X axes of the individual toothprofiles in a horizontal in-out direction with respect to the mandibulararch and special mesiodistally along the mandibular arch.

Because the preferred goal, however, is to position the tips of theteeth in the smoothest arch in an occlusal plane MOC rather than theirgingival aspects in a smooth arch at the mandibular trough MT, (825), ahorizontal distance OFFSET for each tooth is calculated, based on thetooth and the crown long axis inclination LAI determined in step (600).This offset is the horizontal distance from the MTE to the tooth tipswhen their GGP's are placed on the MTE.

For mandibular centrals and laterals and cuspids, the OFFSET iscalculated by dividing, by the tangent of LAI, the vertical distancefrom (1) the intersection of crown long axis CLA and the incisal tip ICto (2) the intersection of CLA and maximum cusp height reference planeMCHP. The vertical distance may be calculated from the IC to the MCHP(equal to the Y coordinate of point IC, producing the incisal centervertical distance ICD.) For mandibular laterals and centrals, ICD equalsMCH. For mandibular cuspids, ICD equals the mandibular cuspid risecomponent, which is MCH+(Total CR)/3 when cuspid rise function occlusionhas been selected. The calculation of the OFFSET for centrals, lateralsand cuspids would thus be as follows for the incisors and laterals:

    OFFSET=ICD/tan(LAI)

(831) For mandibular bicuspids and molars, referring to FIG. 6F, theOFFSET is calculated as the horizontal distance from point P₃ to theintersection of the CLA and the MCHP as follows:

    OFFSET= MCH/tan(LAI)!+HD

where HD equals the horizontal distance from point P₃ to incisal centerpoint ICP.

Then, (835) the mandibular trough placement point MTPP is defined as theintersection of MCHP and CLA, as illustrated in FIGS. 6G and 6H. For thetallest tooth, MTPP is its GCP, as illustrated in FIG. 6I. The MCHP isat the level of the mandibular trough and contains the MTE. The MTPP isthe point on the tooth that is initially placed on the MTE.

Next, referring to FIG. 7B and 7C, the teeth are placed with theirMTPP's on the mandibular trough, one side at a time. To achieve this,(840) the subroutine (2200) is called twice, once for the left side, andonce for the right side, as follows:

The mandibular trough equation MTE is first adjusted for the mandibularcentrals to increase the radii by the amount of the central OFFSET forthat particular tooth, as defined above, to form a mandibular troughoffset curve MO(1) of FIG. 4B. The radii of the MTE referred to arethose of the MTE defined in the circle segment form of the equationgenerated in step (300) with the spline to circle conversion routine(2100). Since the OFFSETs of the teeth differ, the MO may be viewed as adiscontinuous equation when constructed in this manner, made up ofsegments, each containing the tip of one tooth and spacedlabial-lingually from the MTE by the amount of the individual tooth'sOFFSET.

Beginning with the left side, the central is placed, as illustrated inFIG. 7B, by placing its mesial contact point MCP at the intersection ofthe midline ML with the offset curve MO for the tooth. This has theeffect of the placing MTPP of the tooth, which is the intersection ofthe CLA with the MCHP or MT, on the MTE and the incisal tip IC of thetooth on MO₁. The tooth placement on the circle segment form of anequation is explained in detail in the description of the toothplacement routine (2200) below. In the placement of the central, acircle C₁ is constructed with a radius equal to the mesiodistal widthMDW₁ of the central tooth and with the center of the circle C₁ at themesial contact point MCP of the tooth at intersection of the midline MLwith the offset curve MO₁. Then, circle C₂ is constructed with a radiusequal to MDW/2 and with its center coincident with the center of circleC₁. Then, the intersections of trough offset curve MO with the circlesC₁ and C₂ are found, its intersection with the circle C₁ being thedistal contact point DCP of the tooth and its intersection with the C₂being the tooth midpoint TMP of the central tooth. The tooth midpointTMP is here defined as the midpoint of the mesiodistal width of thetooth placed on an archform, which is the intersection of the archformwith a vertical labial-lingual plane that contains the CLA. Thismid-point TMP of the central tooth on the MO is the approximate positionof the incisal tip IC.

Determining the intersections of the circles with the offset troughcurve MO, or expanded mandibular trough, requires identification ofwhich circle sector lines (FIG. 5) the circles C₁ and C₂ intersect.These are identified by comparison of the X coordinates of theintersections with the X coordinates of the distal contact points DCP ofeach of the central teeth to determine which segments of the troughequation will be used, as explained more fully in the description of thetooth placement routine (2200) below.

Finally, a distal contact point line DCPL is constructed for the centraltooth through the DCP, at the intersection of circle C₁ with the MO, andthrough the center of the identified circle segment of the MO, theexpanded MTE, on which the DCP of the tooth lies. This line lies along aradius of the circle segment of the MO curve through the distal contactpoint of the central tooth. Similar lines DTMP are constructed for thecenter of the tooth TMP.

(845) For each of the remaining mandibular teeth on the same side of thearch, in distal sequence, a new mandibular trough offset MO_(I) iscalculated, by expanding the MTE with radii of curvature increased bythe amount of the next tooth's OFFSET and with center of the circles C₁and C₂ moved labially or outwardly from the MTE along the prior tooth'sdistal contact point line DCPL by the amount of the current this tooth'sOFFSET. This is the MCP for the next tooth. Circle C₁ for the tooth isconstructed with a radius equal to the mesiodistal width of the toothand with its center at their center point MCP. Circle C₂ is constructedwith a radius equal to MDW/2 and with centers coincident with circlesC1.

For bicuspids and molars, the tooth midpoints TMP can be considered astheir points P₃. Then, as with the central, the intersections of MO andcircles C₁ and C₂ are calculated for these teeth. The distal contactpoints DCT of these teeth are at the intersections of MO for the toothand the respective C₁ s. The centers of the teeth TMP are at theintersections of MO for the tooth and the respective circles C₂. The MOsector segments which the circles intersect are identified. Selection ofthe segments is made by comparing the X and Y coordinates ofintersections to X and Y coordinates of distal contact points DCPs.Finally, a distal contact point line DCPL is constructed from selectedsegment center to the plane DCP. The same is done for the centers of theteeth TMP.

(848) The substeps (842) are repeated for all of the remainingmandibular teeth on the same side of the arch. Then, (849) substeps(840)-(848) are repeated for the teeth on the opposite side of arch.

(900) Best Fit Mandibular Arch Equation Step:

The above step (800) leaves the crown long axes CIA of the mandibularteeth intersecting the MCHP reference plane, which is at the level ofthe mandibular trough MT at or just below the gingival center points GCPof the teeth, along the mandibular trough equation MTE. Thediscontinuous offset equation MO, however, contains the approximate tipsof the teeth in the occlusal plane MOC, with the teeth irregularlyoffset as represented by the discontinuous MO lines in FIG. 4B. To placethe tips of the teeth into an ideal arch, (900) a final equation forbetter placement of the buccal cusp tips and incisal edges of themandibular teeth in a continuous arch is developed. The development ofthe best fit equation is illustrated in the detailed flowchart of FIG.2M.

When viewed perpendicularly to the occlusal plane as in FIGS. 4B and 7B,it can be seen that the buccal cusp tips and incisal tips of all of theindividual teeth do not lie along either the mandibular trough equationor the same geometrical expansion of that equation. In fact, due tosmall anatomical variations, it is unlikely that the tips will fall onany smooth curve when the tooth CLAs intersect a smooth curve at themandibular trough in the MCHP and the LAIs are preserved. To remedythis, the equation is statistically developed that best fits the cusptips and incisal edges of the individual teeth; a Best Fit Buccal CuspEquation BFBCE. In the formulation of the equation, the coordinates ofthe right and left tooth midpoints TMP, the ICPs or ICs in FIG. 7B, arepreferably averaged. The equation BFBCE may be obtained (910) by use ofpolynomial or other bezier or least square statistical techniques toarrive at a best fit equation. These are available in any of a number ofoff-the-shelf software packages.

Such a BFBCE equation is plotted in FIG. 4B. Once the BFBCE isdetermined, it may be (915) converted to a circle segment equation in amanner such as with the spline to circle conversion routine (2100). Thisequation provides a basis for moving the teeth labially or linguallyfrom the discontinuous offset equation MO to place the tips of themandibular teeth in a smooth arch in the occlusal plane CP, asillustrated in FIG. 7C. To do this, in the next step the profile planeswill be translated bodily in their own horizontal X-directions (which isan X-Y movement in the coordinates of the horizontal planes), movingtheir MTPPs off of the MTE in the MCHP (or MT).

(1000) Mandibular Best Fit Arch Placement Step:

After statistically deriving a best fit equation BFBCE, (1000) positionsof the individual mandibular teeth are calculated to translate thenfacially, either labially or lingually, so that their tips fall on thebest fit curve. This step is illustrated in detail in the flowchart ofFIG. 2N.

To achieve this, (1005) the mesiodistal contact point of the mandibularcentral, the point MCP, as in FIG. 7B, is first placed on theintersection of the midline ML with the BFBCE in the same manner as itwas placed on the MO in step (800). Then (1010) circles C1 and C2, asdefined above, for the tooth are constructed and their intersectionswith the BFBCE curve are found. As with the placement in step (800)above, the intersection of C₁ with BFBCE is the distal contact point DCPof the tooth, and the intersection of C₂ with the BFBCE curve, is thecenter point TMP (which aligns with IC) of the tooth. This, in effect,moves the tooth normal to the circle segment of the BFBCE associatedwith the TMP. Then, (1015) new circles C₁ and C₂ are constructed withcenters at the distal center points DCP and (1020) substeps (1005) and(1015) are repeated for all teeth on the same side of the mandibulararch. Then, (1025) steps (1005) through (1020) are repeated for theteeth on the other side of the mandibular arch. The placement uses thetooth placement routine (2200), the description of which below explainsin detail the placement of the mandibular teeth on the BFBCE.

This step bodily translates the teeth in a generally horizontaldirection, and rotates the teeth of the mandible about their CLAs toplace incisal edges and cusp tips, as determined in step (800), on theBFBCE. With the completion of this step the finished positions of themandibular teeth are calculated and the mandibular occlusion isfinalized. At this point the mandibular occlusion can be envisioned asan ideal setup cast in stone, to which the maxillary occlusion will befitted and related.

The finish positions of the mandibular teeth are illustrated in FIG. 7Cin which the X-Y coordinates are those of the horizontal arch planes. Avertical Z coordinate, perpendicular to the horizontal X-Y plane, isaligned with the Y axes of the individual tooth profile planes. The Xcoordinates of the profile planes are aligned with the labial-lingualdirections La-Li in FIG. 7B.

(1100) Maxillary Tooth Placement Step:

The construction of occlusion requires (1100) the fitting of themaxillary teeth to the already positioned mandibular teeth. This isaccomplished by deriving a modified best fit buccal cusp equation BFBCEfor the maxillary teeth in the step illustrated in detail in theflowchart of FIG. 2O. Unlike with the mandibular teeth, with themaxillary teeth, the cusp tips of the posterior teeth and incisal edgesof the anterior teeth are not set in a single arch. The maxillary teethare rather set: (1) with the central groove-marginal ridge points of themaxillary bicuspids and molars on the BFBCE, (2) with the maxillaryanteriors spaced labially off of the BFBCE to allow for incisal overlapand a clearance between the lingual surfaces thereof and the labialsurfaces of the mandibular teeth, and (3) with the cuspid tips in thearch generally between the first maxillary bicuspid and the lateralincisor. The arches on which the maxillary teeth are placed asillustrated in FIG. 4C, as explained above.

For the maxillary incisors, the modification of the BFBCE first involvesan averaging the distances from point P₂ to point P₃ on the mandibularincisor incisal edge, and dividing by two, to locate the arch that willcontain the labial surface of the tooth adjacent the incisal centerpoint ICP of the tooth, which is generally the point P₃. This produces auniform distance from the best fit equation to the contact point of thefacial surface on the labial side of the mandibular anterior teeth withthe facial point on the lingual side of the maxillary anterior teeth. Anadditional distance, of typically one-quarter millimeter, is added tothe averaged distance to provide a slight Clearance between the upperand lower anterior teeth. This is illustrated in FIG. 7D.

The maxillary anterior dentition is set for vertical position relativeto the occlusal plane MOC according to occlusion criteria selected toprovide a predetermined overlap. From the cuspid rise calculation ofstep (700), the vertical positions of the maxillary cuspids are knownrelative to the mandibular occlusal plane MOC. For maxillary lateralsand centrals, the vertical positions provide the overlaps according tothe prescribed criteria, putting their lingual facial contact pointswith their mandibular counterparts on the MOC plane. All teeth areinclined at the prescribed crown long axis CLA inclination values LAIfrom Table 1 in step (600).

In the (1100) placement of the teeth of the maxilla, or upper jaw 24,with respect to those of the mandibular, or lower jaw 22, (1105) threearch forms are mathematically defined. These are (1106) the maxillaryanterior arch form MAAF, (1110) the central groove marginal ridge archform CGMRAF, and (1115) the maxillary cuspid arch form MCHF, asillustrated in FIG. 4B. The MAAF is established to position themaxillary incisors with respect to the BFBCE so that their lingual facescontact or clear the labial faces of the mandibular incisors. The CGMRAFis established separate from the MAAF because the maxillary bicuspidsand molars contact their mandibular counterparts with their centralgroove marginal ridge intersection points juxtaposed on the mandibularbuccal cusps. The MCAF is established separate from the MAAF and theCGMRAF because the cuspids have a still different relation to theirmandibular counterparts.

(1106) Location of the MAAF relative to the BFBCE requires a circlesegment radius expansion of the BFBCE equation such that the lingualsurfaces of the maxillary incisors, after being adjusted vertically toprovide a predetermined overlap, will contact the labial face of themandibular incisors at points spaced labially from the BFBCE with thepredetermined Clearance. This expansion is calculated as the averagedistance between points P₃ and P₂ on the four maxillary incisors andadding the predetermined Clearance of typically 0.25 mm. This expansion,so calculated, is added to the BFBCE circle segment radii to define themaxillary anterior contact arch form MAAF. The MAAF is thus alsoexpressed as a circle segment equation.

The calculation of the amount of circle segment radius expansion of theBFBCE needed to define the MAAF is made at the midpoint of themesiodistal width of either maxillary central, TMP₁ in FIG. 4C. Thiswould be the intersection with BFBCE of circle C₂ in FIG. 7C. The toothis placed on the maxillary contact arch form equation MAAF such that themesial contact point of the tooth is on intersection of the midline MLand the maxillary contact arch form MAAF (FIG. 4C). (1108) The MAAF isdefined as follows with respect to upper laterals and centrals:##EQU13## where: t=number of teeth (4),

Avg=2 (to find midpoint), and

Clearance=0.25 mm, typically.

P₂ and P₃ are points on the maxillary central as defined in step (600).As described above, the crown long axes CLA of these teeth are angulatedrelative to the occlusal plane at the crown long axis seed values statedin Table 1.

(1109) The tooth placement proceeds in accordance with the toothplacement routine (2200) described below. The placement positions thelingual faces of the central teeth on the MAAF, with the central mesialcontact point MCP₁ on ML. The midpoint TMP₂ of the mesiodistal width ofthe next maxillary tooth is then placed on the maxillary contact archequation MAAF such that the mesial contact point MCP₂ touches a linenormal to the curve MAAF and through the distal contact point DCP₁ ofthe previous tooth. This procedure applies on one side of the occlusionup to the cuspid. The other maxillary side is constructed similarly.

The next substep in the construction of the maxillary occlusion is(1110) the definition of the location of the arch for horizontalplacement of the posterior teeth. The teeth are again set at the LAIvalues of Table 1 from step (600). (1111) The intersections of themarginal ridge and the central groove, which, if not separately selectedin step (600) may be taken as point P₅ in FIG. 6C, are placed over thebuccal cusp of the appropriate mandibular tooth whose cusps werepreviously positioned on the best fit buccal cusp equation BFBCE. Thus,the CGMRAF coincides with the BCBFE as shown in FIG. 4B.

For the maxillary cuspids, (1115) the cusp tips are placed on somesmooth arch between the he MAAF and the CGMRAF. Preferably, their tipsare placed on the BFBCE expanded by the average of the distancestherefrom to the incisal tip of the lateral and to the buccal cusp tipsof the first maxillary bicuspids. This labial distance from this pointto the buccal cusp tip of the first bicuspid may alternatively be usedto place the distal contact point of the cuspid, with its mesial contactpoint in contact with the distal contact point of the lateral. The pointto which the BFBCE must be expanded to locate the buccal cusp tip of thefirst bicuspid for the two above alternatives is P_(3X) (U,4)-P_(5X)(U,4). The cuspids will thereby be spaced out from the BFBCE by theaverage of a distance equal to the horizontal or X distance from P₅ toP₃ on the first maxillary molar, as illustrated in FIG. 6C, and theMAAF.

Alternatively, the cuspids may be placed with their mesial contactpoints MCP₃ on the MAAF and with their distal contact points DCP in linewith the mesial contact points or with the buccal cusp tips of the firstmaxillary bicuspids.

A third alternative in placing the cuspids is to use the same criteriafor clearance with the mandibular teeth used for the definition of theMAAF. Following the determination of the MCAF, the cuspids placedadjacent the laterals with the tips thereof on the MCAF, followed by thesuccessive placement of the posterior teeth with the marginal ridgesthereof on the CGMRAF (BFBCE), all according to routine (2200).

In relating the profile and archform drawings and equations above, itshould be noted that the X dimension of the profiles on which P₃ and P₅are defined are vertical planes, and that the X direction in theseplanes corresponds to the labial direction in the horizontal planes ofthe archforms, as was explained for the mandibular teeth in connectionwith FIG. 7C. Thus, addition of an X component of a point on a toothprofile to an archform curve results in a labial expansion of thearchform, or an increase in the radius of the corresponding circlesegment of the archform circle series equation.

At this point, information from the prescription 27 from theorthodontist 14 is retrieved to determine (1120) which maxillaryanterior vertical occlusion method has been selected. The methods mayinclude, for example, (1121) Roth occlusion, (1122) Ricketts occlusion,or (1123) the preferred method, referred to by the inventors as Elanocclusion. These are discussed below.

Where (1121) Roth occlusion has been selected, the maxillary cuspidswill extend a distance CR_(U3) equal to the cuspid rise CR below theocclusal plane MOC, and for laterals and centrals, the teeth will extenda distance CR_(U2) equal to 0.5 the cuspid rise beyond the occlusalplane, as illustrated in FIG. 7D. From step (725), the treatment isselected to apply either group function or cuspid rise function, and therespective cuspid rise quantities for maxillary cuspids are determined.From the lowest point on buccal (facial) cusp, a distance is measurevertically upward equal to 0.5 CR to find the intersection of occlusalplane MOC and central and lateral teeth. If two profiles were taken, theprofile that includes marginal ridges is used. The intersections of MOCwith each maxillary incisor are defined as follows:

Facial intersection with MOC=FIMOC,

Lingual intersection with MOC=LIMOC,

The distance from LIMOC to FIMOC, DLF, is computed as follows:

    DLF=X.sub.FIMOC -X.sub.LIMOC,

where LIMOC is the contact point with MAAF.

Where (1122) Ricketts occlusion is prescribed, the maxillary cuspidsalso extend below the MOC by a distance CR_(U3) equal to the cuspid riseCR. The laterals are positioned such that the tips are the distanceCR_(U2) of 1.0 mm above the cuspid tips, and the distance CR_(U1) issuch that the tips of the centrals are 0.5 mm above the cuspid tips.From step (725), in which either group function or cuspid rise functionwere selected, the respective cuspid rise quantities are applied for themaxillary cuspids. Then, from lowest point on buccal (facial) cusp, adistance of 1.0 mm is measured upward on the laterals and a distance of0.4 mm is measured upward on centrals to find the intersection of MOCwith the central and lateral teeth. If two profiles were taken, aprofile that includes the marginal ridges is used. A line is thenconstructed through the points on the buccal cusps parallel to the MOC,The intersections with the teeth are defined as follows:

Facial intersection with MOC=FIMOC

Lingual intersection with MOC=LIMOC

Distance DLF from LIMOC to FIMOC=X_(FIMOC) -X_(LIMOC),

where LIMOC is contact point with MAAF.

Where (1123) Elan occlusion has been selected, the maxillary cuspidswill extend a distance CR_(U3) equal to 0.67 of the cuspid rise CR belowthe occlusal plane MOC, laterals extend a distance CR_(U2) equal to 0.33of the cuspid rise CR below the plane MOC, and the centrals extend adistance CR_(U1) equal to 0.50 of the cuspid rise CR below the planeMOC. As with the above, from step (725), in which either group functionor cuspid rise function were selected, the respective cuspid risequantities are applied for the maxillary cuspids. Then, from the lowestpoint on buccal (facial) cusp, a distance of 0.33 of the cuspid rise CRis measured upward on the laterals, and a distance of 0.50 of the cuspidrise CR is measured upward on the centrals, and the intersection of theteeth with the plane MOC is found. If two profiles were taken, a profilethat includes marginal ridges is used. The MOC plane and theintersections with the teeth are defined as follows, as illustrated onthe cuspid in FIG. 7D:

Facial intersection with MOC=FIMOC.

Lingual intersection with MOC=LIMOC.

Distance DLF from LIMOC to FIMOC=X_(FIMOC) -X_(LIMOC),

LIMOC is contact point with MAAF.

The (1125) elected horizontal occlusion is selected. If (1126) the Rothmaxillary anterior horizontal occlusion has been selected, no furtherchanges are required. This results in the lingual surfaces of the teethforming a smooth arc. If (1127) the Ricketts maxillary anteriorhorizontal occlusion has been selected, changes are made to cause thelabial surfaces of the teeth to form a smooth arc. This requires findingthe largest DLF, or LIMOC-FIMOC distance for the centrals, subtractingthe other LIMOC-FIMOC distances of the incisors from this largestdistance, adding the respective differences to each tooth to extend theLIMOC point lingually along line LIMOC-FIMOC, and establishing a newpoint at which the LIMOC is to intersect the MOC.

If (1128) the Elan horizontal occlusion is selected, which is thepreferred and illustrated embodiment, the horizontal tooth placementproceeds as set forth below. Because, given the overlap of the maxillaryincisors, the labial-lingual thicknesses of the anterior teeth aregreater in the plane of occlusion than the distance P₃ -P₂ used tocalculate the MAAF and the MCAF, offsets must be calculated and themaxillary teeth placed again on the offset versions of these archforms.

First, in calculating the positions of the teeth to provide thehorizontal occlusion, (1130) a distance is calculated from LIMOC to ICPfor the maxillary centrals and the laterals. This distance is referredto as the maxillary anterior offset MAO, thus: ##EQU14##

    MAO=LIMOC.sub.X -ICP.sub.X,

(1135) The maxillary first bicuspid offset MBO is calculated:

    MBO=P.sub.5X -P.sub.3X,

(1140) The maxillary tooth positions are then recalculated, one side ata time, with respect to the offset maxillary arch forms defined abovethat contain the buccal cusp tips and incisal edges of the maxillaryteeth. This is achieved by sending the relevant parameters to theplacement routine (2200) and calculating placement in the same manner asshown in FIG. 7B for the mandibular teeth. For the maxillary centrals,(1141) MAAF is adjusted such that the MAAF radii are increased by theamount of the MILO. This curve is now called maxillary contact archformoffset MAAFO and is illustrated in FIG. 4C.

Calculation of the positions of the maxillary incisors on the MAAFO,preferably in accordance with the tooth placement routine (2200), closesthe spaces between the teeth that results from expanding MAAF to MAAFO.

The intersection of MAAFO and the arch midline ML is the mesial contactpoint MCP of the tooth. A circle C₁ is constructed with a radius equalto the mesiodistal width MDW of the central incisor. Its center is atthe intersection point of MAAFO and ML. The intersection of the circleC₁ with MAAFO is the distal contact point DCP. Then, circle C₂ isconstructed with a radius equal to MDW/2, that is half the mesiodistalwidth MDW. Its center is coincidental with that of C₁. The intersectionof the circle C₂ with the MAFFO curve is the mid-point of tooth TMP andthe incisal center point ICP.

The intersection of MAAFO and circles C₁ and C₂ are then constructed.The curve defined by MAAFO and the intersection of circle C₁ is thedistal contact point DCP. The intersections of MAAFO and MAAFO circlesegment lines are found. The X coordinates of the intersections arecompared to the X coordinates of DCP to determine which segment's centerwill be used.

A distal contact point line DCPL is constructed from the selectedsegment center to the DCP. Similarly a center of tooth line TMPL isconstructed from the sector center to the TMP. Thus, the tooth LIMOC ison MAAF and the tooth mesiodistal width line is on the MAAFO arch. Thelocation of FIMOC is accordingly determined by adding DFL to the MAFFOcircle segment radius through the TMP.

The MAAFO, like the MO for the mandibular teeth, is discontinuous, withthe archform being offset differently for the different maxillary teeth.Accordingly, for the maxillary laterals, the prior MAAFO is replacedwith the MAAF adjusted such that the MAAF radii are increased by amountof MAO for lateral. The tooth's MCP is the tooth's MAO distance from theMAAF along the prior tooth's distal contact point line DCPL. Circle C₁is constructed with a radius the mesiodistal width of the tooth and witha center at the tooth's MCP. The intersection of C₁ with the MAAFO isthe tooth's DCP. Circle C₂ is constructed with a radius equal to half ofthe tooth's MDW and with a center coincident with that of circle C₁. Theintersection of circle C₂ with MAAFO is the tooth's ICP.

Then, the intersections of MAAFO and the MAAFO sector lines are found.The X and Y coordinates of intersections are compared to the X and Ycoordinates of DCP to determine which segment's center will be used. Adistal contact point line DCP is constructed from the selected segmentcenter to the DCP. Similarly a center of tooth line TMPL is constructedfrom the sector to the TMP.

For the maxillary cuspids, the prior MAAFO is eliminated. A new archform, the maxillary cuspid arch form MCAF, is computed to place thecuspid between the lateral and the first bicuspid. In one preferredapproach, the MCAF is constructed offset from the BFBCE by the averageof the OFFSETs of the first bicuspid and the lateral, as calculated insubstep (1135) above. With exception of a new arch radius, the cuspid isplaced as above.

For the maxillary bicuspids and molars, the arch form CGMRAF, which isthe BFBCE, is offset by MBO. CGMRAF is adjusted by adding MBO for therespective teeth. The cuspid tips on the MCAF, which was offset from theBFBCE to align with the buccal cusp tips of the first bicuspids in(1115) above, are thus in line with the posterior buccal cusp tips. Fromthe cuspid DCP, circles C₁ and C₂ are constructed and DCPLs areestablished. This sequence is repeated for remainder of the teeth,completing the relation of the maxillary and mandibular occlusions. Thefinish positions of the maxillary teeth are illustrated FIG. 4D.

At this point, the final positions of the maxillary teeth have beencalculated, and thus, the finish positions of all of the teeth.

Appliance Design Procedure (96)

The appliance design procedure includes the steps of (1200) determiningthe location of the mandibular archwire plane relative to the calculatedfinish positions of the mandibular teeth, (1300) calculating the angleof each mandibular bracket slot relative to the mounting surface of therespective tooth, (1400) determining the location of the maxillaryarchwire plane relative to the calculated finish positions of themaxillary teeth, (1500) calculating the angle of each maxillary bracketslot relative to the mounting surface of the respective tooth, (1600)calculating the shape of the mandibular archwire and the slot in-outdimension of each mandibular bracket, (1700) calculating the shape ofthe maxillary archwire and the slot in-out dimension of each maxillarybracket, and (1800) calculating the contours of bracket placement jigsfor each tooth.

(1200) Mandibular Archwire Plane Step:

The next step is (1200) to establish the position of the archwire planefor the mandibular teeth, which is illustrated in detail in theflowchart of FIG. 2P. The archwire plane can be located in an infinitenumber of vertical positions since the brackets and archwire will bedesigned to accommodate any chosen location. Since the overlap of themaxillary teeth is known, for labial bracket placement, the mandibulararchwire plane is set to provide bracket clearance for the maxillaryteeth in the finished occlusion. For lingual bracket placement, thisconsideration is given to the maxillary archwire plane instead, in step(1300) below.

Since the maxillary teeth do not pose a bracket interference dilemmawith labial bracket placement, the brackets can be positioned for easeof placement, cosmetic considerations and gingival health. This appliesto the mandibular bracket positioning where lingual bracket placement isused. Typically, these brackets are located more centrally than thebrackets of the other arch.

More particularly, as illustrated in the flowchart of FIG. 2P and FIG.8, (1200) to establish the archwire plane, (1205) the selected verticalocclusion and respective vertical overlap from MOC for cuspids, lateralsand centrals is recalled from (1110). Then, (1210) with the informationfrom (705), the buccal cusp height BCH is recalled for each bicuspid andmolar. Next, (1215) the maximum BCH or anterior vertical overlap ischosen as the maximum vertical overlap MVO. Then, (1220) a distanceequal to the MVO is measured downward from the MOC. Finally, (1225) halfof the bracket height (typically 3.0 mm) plus an additional 0.75 mm isadded for occlusal clearance. This defines the mandibular archwire planeMAWP. This places brackets as occlusal as possible with an 0.75 mmclearance from the worst case from the maxillary occlusion.

(1300) Mandibular Slot Inclination Step:

Once the archwire planes have been defined with respect to the teeth, asillustrated in the flowchart of FIG. 2Q, (1300) the angle between thebracket mounting surface of the teeth and archwire plane is determined.This angle minus 90° is the facial torque or inclination angle to beformed into the brackets. This also defines the bracket slot placementheight which is the distance from the top of the incisal edge to thearchwire plane. This distance is calculated perpendicular to thearchwire plane.

Slotless bracket bodies (vanilla brackets) have now been positionedappropriately. A smooth archwire is then designed such that it will passthrough the bodies of the brackets. The archwire must not cut too deeplyinto the bracket or pass even partially outside the face of thebrackets. Brackets are chosen having different heights according toneed. Without modifying buccal tube assemblies, standard bracketdistances from the tooth surface to the center of the slot may be usedas a seed values. The archwire equation is then mathematically derivedfrom cubic spline and tangential circle techniques as previouslydescribed and provided in the routines (2000) and (2100). Both archwiresare developed similarly.

Bracket angle determination (1300), more particularly, is achieved by(1305) taking the intersection of the MAWP and labial (buccal) surfaceof each mandibular tooth in the case of labial appliances, and theintersection of the MAWP with the lingual surface of each tooth in thecase of lingual appliances. Then, (1310) circles are constructed withcenters at the intersections and with diameters that represent theoccluso-gingival (vertical) dimensions of the bracket bonding pad(typically 3.0 mm). Then, (1315) X,Y coordinates of the circleintersections with labial (buccal) tooth surface are taken, and, withthe equations:

    R.sup.2 =(X.sub.1 -h).sup.2 +(Y.sub.1 -K).sup.2

    Y.sub.2 =mX.sub.2 +b.sub.2

    Y.sub.3 =mX.sub.3 +b.sub.3

(1320) The slopes between the points of intersection are calculated toproduce the facial inclination angle FIA, where:

    h,k=coordinates of circle center

    X.sub.1, Y.sub.2,b.sub.2 =definition of first line segment

    X.sub.3, Y.sub.3,b.sub.3 =definition of second line segment

Then, as illustrated in FIG. 8A for labial appliances, π/2 radians arethen subtracted to produce the slot inclination angle SIA: ##EQU15##

    SIA=FIA-π/2

(1400) Maxillary Archwire Plane Step:

The next step is (1400) locating the maxillary archwire plane asillustrated in the flowchart of FIG. 2R and diagram of FIG. 8. For themaxillary centrals, this involves (1405) finding the vertical distancefrom incisal edge to point P₄. (1410) The smallest value is selected anddivided by two to produce the slot placement height for the maxillarycentrals. (1415) For terminal maxillary bicuspids the vertical distancefrom buccal cusp to point P₄ is found. (1420) Again, the smallest valueis selected and divided by two. This produces the slot placement heightSPH for the terminal maxillary bicuspids.

For maxillary centrals, (1425) the Y value of FIMOC is subtracted fromthe Y value for the slot placement height SPH. This is the distance fromMOC to the slot centerline. For terminal maxillary bicuspids, (1430) theY value of MOC is subtracted from the Y value for the slot placementheight SPH. This is the distance from MOC to the slot centerline. Then,(1435) the SPH for the terminal bicuspid from SPH for the maxillarycentrals. This is elevation change DH of the maxillary archwire relativeto the MOC from the centrals to the terminal maxillary bicuspids. (1440)The elevation of the maxillary archwire MXAWP from the MOC, or archwireheight AHT on each tooth, is calculated as follows:

    AHT=K+DH+SPH-MOC.sub.Y +Vertical overlap from (1110)

where K is the conversion factor from Table 3.

                  TABLE 3                                                         ______________________________________                                                                    Extraction                                                           Non-     (e.g. 2nd)                                        Tooth Type         Extraction                                                                             Biscuspid)                                        ______________________________________                                        Maxillary Central  0.0      0.0                                               Maxillary Lateral  -0.19    -0.28                                             Maxillary Cuspid   -0.42    -0.62                                             Maxillary First Bicuspid                                                                         -0.68    -1.00                                             Maxillary Second Bicuspid                                                                        -1.00    NA                                                Maxillary First Molar                                                                            -1.32    -1.46                                             ______________________________________                                    

(1500) Maxillary Slot Inclination Step:

Once the archwire plane is determined, as illustrated in the flowchartof FIG. 2S, (1500) the slot inclination angle SAI for each of themaxillary tooth brackets is determined in a manner similar to the slotinclination determination step for the mandibular brackets (1300). Thisstep (1505) begins by finding the intersection of the maxillary archwireplane MXAWP with the labial or buccal surface of each maxillary tooth.Then, (1510) circles are described, for each maxillary tooth, havingcenters at this intersection point and having diameters equal to theoccluso-gingival, or vertical, dimensions of the bracket bonding pad,which is typically 4.0 mm. From these circles, (1515) X,Y coordinates ofthe intersections of the circles with the labial or buccal tooth surfaceare found, as follows:

    R.sup.2 =(X.sub.1 -h).sup.2 +(Y.sub.1 -k).sup.2

    Y.sub.2 =mX.sub.2 +b.sub.2

    Y.sub.3 =mX.sub.3 +b.sub.3

Where:

h,k=coordinates of the circle center

X₁, Y₁ =possible coordinates on the circle

X₂, Y₂,b₂ =definition of a first line segment

X₃, Y₃,b₃ =definition of a second line segment

Then, as illustrated in FIG. 8A, (1520) π/2 radians are then subtractedto produce the slot inclination angle SIA: ##EQU16## (1600) MandibularArchwire and Slot Depth Step:

The next step, as illustrated in the flowchart of FIG. 2T, is (1600) todetermine the mandibular archwire and bracket in-out dimension. First,(1605) the circle segment of the BFBCE with which the ICP of the rightcentral is associated is determined, as illustrated in FIG. 8B. Then,(1610) the incisal center point and circle segment center point planeICPCDCPP is created normal to the arch planes. An incisal center pointline ICPL is struck that will pass through the ICP and a particularcircle segment center point CSCP associated with the tooth. Then (1615)the Pythagorean distance PD from CSCP to ICP is determined. Then, (1620)viewing the tooth in the ICPCSCPP, as illustrated in FIG. 8C, a line NLis struck normal to the BFBCE plane through the ICP, which is theintersection of CLA and BFBCE. Next, (1625) still viewing the tooth inthis plane, the intersection point XP of NL and MAWP is determined.

Still viewing the tooth in the ICPCSCPP, (1630) the X distance XD to thelabial surface of the tooth from the XP is determined, and (1635) PD isadded to XD and the lower limit of the bracket slot LLBS. The LLBS is adistance associated with the particular bracket that will be placed onthis tooth. It is the deepest slot allowable for that bracket. Then, thelower limit LL is calculated thus:

    LL=PD+XD+LLBS

Similarly, (1640) PD is added to the XD and the upper limit of thebracket slot ULBS. The ULBS is also a distance associated with theparticular bracket that will be placed on this tooth. It is theshallowest slot allowable for that bracket. The, the upper limit UL iscalculated thus:

    UL=PD+XD+ULBS

(1645) Then, viewing the mandibular occlusion in a plan view and movingout along the ICPL from its CSCP by the LL distance, X and Y points,AWLL_(X),Y, are determined relative to an origin at the intersection ofBFBCE and the mandibular midline ML. Then,(1650) viewing the mandibularocclusion in a plan view and moving out along the ICPL from its CSCP bythe UL distance, X and Y points, AWUL_(X),Y are determined relative tothe intersection of BFBCE and the mandibular midline ML. Then, (1655)the mid-point of AWLL_(X),Y and AWUL_(X<Y) is found and steps (1605)through (1650) are then repeated for all mandibular teeth.

Then, (1660) the average mid-point and distance from right to left iscalculated to force mandibular archwire symmetry: ##EQU17## Where:S_(X),Y is the symmetricalized point.

MP is the mid-point of BCBCE.

PR is a point on the right side of the midline.

PL is a point on the left side of the midline.

The smoothest curve SC that will pass between all AWLL_(X),Y andAWUL_(X),Y points is then determined, as illustrated in FIG. 4E. This isaccomplished by the following procedure:

a) The mid-point of each AWLL_(X),Y and AWUK_(X),Y pair is found.

b) Then, as described above, a cubic spline equation is passed throughthese points.

c) The existence of any inflection points is determined.

d) The curve with the least variation in radius changes along the curveis considered the smoothest curve. Preferably, it has no inflectionpoints. If there are one or more inflection points, a logicalalternative bracket solution will be derived based upon where theinflection occurred. Then, (1665) the intersection point XSCICPL of themandibular right central's ICPL is determined as well the smoothestcurve as defined above in substep (1660). Next, (1670) the in-out IO ofthat particular tooth is determined as the distance along ICPL from ICPto XSCICPL minus that tooths' XD. Then, (1675) steps (1665) and (1670)are repeated until all in-out dimensions are calculated.

Finally, (1675) all XCSICPL points are passed into the cubic splineroutine (2000) and to circle routine (2100) and (1680) all circlesegment information gathered therefrom are converted to linear distanceLD moves needed to bend the appropriate wire, as will be furtherexplained in connection with the wire bending step (3200) below. Thebracket slot cutting is described in connection with step (3000) below.

(1700) Maxillary Archwire and Slot Depth Step:

The next step, as illustrated in the flowchart of FIG. 2U, is (1700) todetermine the maxillary archwire and bracket in-out dimension. As withthe mandibular determination step (1600), (1705) the circle segment ofthe BFBCE with which the ICP of the right central is associated isdetermined. The step is similar to that for the mandibular slot in-outdimension calculation of FIGS. 4E and 8C, except that the maxillarycentrals and laterals are associated with the MAAF rather than theBFBCE, the maxillary cuspids are associated with MCAF, and teethposterior to the cuspid are associated with the BFBCE.

The calculation proceeds with (1710) the incisal center point and circlesegment center point plane ICPCDCPP being created, with a line beingstruck that will pass through the incisal center point line ICPL whichwill pass through the ICP and a particular circle segment center pointCSCP associated with the tooth. The plane passing through the ICP andthe CSCP and normal to the mandibular trough MT is the ICPCSCPP. Then(1715) the Pythagorean distance PD from CSCP to ICP is determined. Then,(1720) viewing the tooth in the ICPCSCPP, a line NL is struck normal tothe BFBCE through the intersection of CLA and BFBCE. Next, (1725) stillviewing the tooth in this plane, the intersection point XP of NL andMAWP is determined.

Still viewing the tooth in the ICPCSCPP, (1730) the X distance XD to thelabial surface of the tooth from the XP is determined, and (1735) PD isadded to XD and the lower limit of the bracket slot LLBS. The LLBS is adistance associated with the particular bracket that will be placed onthis tooth. It is the deepest slot allowable for that bracket. Then, thelower limit LL is calculated thus:

    LL=PD+XD+LLBS

Similarly, (1740) PD is added to the XD and the upper limit of thebracket slot ULBS. The ULBS is also a distance associated with theparticular bracket that will be placed on this tooth. It is theshallowest slot allowable for that bracket. The, the upper limit UL iscalculated thus:

    UL=PD+XD+ULBS

(1745) Then, viewing the mandibular occlusion in a plan view and movingout along the ICPL from its CSCP by the LL distance, X and Y points,AWLL_(X),Y, are determined relative to the intersection of BFBCE and themandibular midline ML. Then, (1750) viewing the mandibular occlusion ina plan view and moving out along the ICPL from its CSCP by the ULdistance, X and Y points, AWUL_(X),Y are determined relative to theintersection of BFBCE and the mandibular midline ML. Then, (1755) Themid-point of AWLL_(X),Y and AWLL_(X),Y is found and steps (1705) through(1750) are then repeated for all mandibular teeth.

Then, (1760) the average mid-point and distance from right to left iscalculated to force mandibular archwire symmetry: ##EQU18## Where:S_(X),Y =the symmetricalized point.

MP=the mid-point of BCBCE.

PR=a point on the right side of the midline.

PL=a point on the left side of the midline.

Then the smoothest curve SC that will pass between all AWLL_(X),Y andAWUL_(X),Y points is determined. This is accomplished by the followingprocedure:

a) The mid-point of each AWLL_(X),Y and AWUK_(X),Y pair is found.

b) Then, as described above, a cubic spline equation is passed throughthese points.

c) The existence of any inflection points is determined.

d) If there are no inflection points, this is considered the smoothestcurve. If there is an inflection point, a logical alternative bracketsolution will be derived based upon where the inflection occurred. Therelevant information necessary to determine a new pair of AWLL_(X),Y andAWUL_(X),Y and their midpoints is undertaken. It should be noted thatthere are varying LLBS and ULBS possibilities available for each tooth.

Then, (1765) the intersection point XSCICPL of the mandibular rightcentral's ICPL is determined as well the smoothest curve as definedabove in substep (1760). Next, (1770) the in-out of that particulartooth is determined as the distance along ICPL from ICP to XSCICPL minusthat tooths' XD. Then, (1775) steps (1765) and (1770) are repeated untilall in-out dimensions are calculated.

Finally, (1775) all XCSICPL points are passed into the spline to circleprogram and (1780) all circle segment information gathered therefrom areconverted to linear distance LD moves needed to bend the appropriatewire, as will be further explained in connection with the wire bendingstep (3200) below. The bracket slot cutting is described in thediscussion of step (3000) below.

(1800) Placement Jig Design Step:

With the shapes of the individual teeth determined, their finishpositions calculated, and the brackets designed and their places on theindividual teeth determined, the information necessary for the design ofbracket placement jigs to aid the orthodontist in positioning thebrackets in their proper positions on the individual teeth is available.In the preferred embodiment of the invention, the design of theplacement jigs is carried out in the software associated with the jigmanufacturing step (3500) described below, following a loading of theappropriate files with the necessary data from the calculationsdescribed above into the manufacturing control computer 30c. Anabbreviated presentation of the jig design substeps is set forth in theflowchart of FIG. 2V.

Referring to FIG. 2V, (1805) a file containing data of the individualtooth profiles, the archwire plane location including data relating eachof the tooth profiles to the relevant archwire plane, the bracketprofiles relevant to each tooth, and the bracket design data includingthe slot size, inclination and depth, are prepared. Then, (1810) thetools that will form the jig are determined, and (1815) clearances areestablished. Then, (1820) data needed for instructions to cut aninternal profile into each jig is assembled to hold a bracket and tolocate the bracket at the proper position on the tooth by precisefitting of the jig over the tooth profile along a labial-lingual planethrough the tooth midpoint TMP.

The details of the jig design step, as it is performed along with thejig manufacturing step, is described in detail in connection with thedescription of the flowchart of FIG. 2Z under step (3500) below.

Subroutines

Three subroutines are used in calculating various archforms andcalculating the positions of the teeth thereon. These are (2000) thecubic spline equation curve calculation subroutine, (2100) the splineequation to circle segment equation conversion subroutine, and (2200)the tooth placement subroutine. These are illustrated in the flowchartof FIG. 2W.

(2000) Cubic Spline Equation Fitting Subroutine:

In the cubic spline interpolation, symmetrical data points areinterpolated and a cubic spline equation is derived. As illustrated inFIG. 5A, a symmetrical mandibular trough or cubic spline equation SMT isshown for one side of the lower jaw. In FIG. 5A, the point M_(X),M_(Y)represents the intersection of the curve and the midline ML. The pointsSI_(X),SI_(Y) for I=1 to 6 represent the symmetricized points X_(ML)referred to above.

The cubic spline method uses a cubis (3rd degree) polynomial tointerpolate between each pair of data points. A different polynomial isused for each interval, and each one is constrained to pass through theoriginal data points with the same slope as the data. At these points,slopes are computed by finding the slope of the parabola that passesthrough each data point and its two nearest neighbors.

The iterations necessary to compute the cubic polynomial are as follows:

1) For each data point, the X and Y coordinates are made equal to zeroand all other data points evaluated relative to this new original.

2) The slopes of the cubic spline are computed by first computing thecoefficients of the above described parabola, then a first point of aslope array is filled followed by the remaining points through the finalslope array point.

3) The spline coefficients are computed.

4) The polynomial is evaluated.

These steps are described in Science and Engineering Programs, Apple IIEdition, Edited by John Hellborn, and published by Asborne/McGraw-Hill.Copyright, 1981, McGraw-Hill, Inc., and incorporated herein byreference.

Once the polynomial has been evaluated, it is possible to acquireadditional data points. A Y value can be determined for any given Xvalue, with the constraint that additional data points be within theupper and lower limits of the original X values. The followingiterations are performed before circle conversion:

1) Determination of X and Y points on each side of the original datapoints. This is done by taking X points that are one thousandth (0.001)to each side of original X data points. Then X values two thousandths(0.002) less than the last data point are taken. Then Y points aredetermined for each arrayed X point by evaluation of the polynomialequation discussed above. Then the Y points of the array are calculated.

2) The slope array is then filled with slopes corresponding to datapoints on either side of the original data points.

3) The slope of the curve at each of the original data points iscalculated. This involves retrieving X and Y points on either side oforiginal data points, and calculating the slope at the original datapoints using the Point Slope method according to: ##EQU19## Where:SLOPE=the slope of the curve at that point.

X1=the X point 0.001 to left of original data point.

Y1=the Y point associated with X1.

X2=the X point 0.001 to right of original data point.

Y2=the Y point associated with X2.

The slope is calculated using the arrayed point that is 0.002 less thanthe last data point and the last data point, and the slope is calculatedusing the point slope method as all array slopes are calculated.

(2100) Circle Segment Conversion Subroutine:

The circle segment conversion typically fits two circle segments intoone spline segment. A spline segment is defined as the interpolatedcubic spline equation which describes the shape of the curve between twooriginal data points. A circle segment is defined as the arc associatedwith a beginning point, or end point, and the slope of tangency at thatpoint. Two configurations of circle segments are possible whenconverting a spline segment into two circle segments, one where thefirst circle is larger than the second (FIG. 5B) and the other where thefirst circle is smaller than the second circle FIG. 5C, the variables inwhich are identified below. The iterations necessary to convert a splinesegment into two circle segments are illustrated in FIG. 5D in which:

P1_(X),P1_(Y) =the beginning point of spline segment

P2_(X),P2_(Y) =end point of spline segment

MT1=tangent slope of spline at point P1_(X),P1_(Y)

MN1=normal slope of MT1

MT2=tangent slope at point P2_(X),P2_(Y)

MN2=normal slope of MN2

P3_(X),P3_(Y) =intersection of a line through point P1_(X),P1_(Y) with aslope of MT1 and a line though point P2_(X),P2_(Y) with a slope of MT2

CL=a Cord Line, a line connecting points P1_(X),P1_(Y) and P2_(X),P2_(Y)

CNL=a Cord Normal Line, a line normal to CL through P3_(X),P3_(Y)

hs,ks=the center of the smaller of the two circle segments

The iterations to convert a spline segment into two circle segments are,as follows:

1) Determine MN1 and MN2. They are the negative inverse of MN1 and MT2,respectively.

2) Determine the intersection point P3_(X),P3_(Y).

3) Determine the slope of the CL.

4) Determine the slope of CLN.

5) Determine the distance from P1_(X),P1_(Y) to P3_(X),P3_(Y). This isdefined as test one.

6) Determine the distance from P2_(X),P2_(Y) to P3_(X),P3_(Y). This isdefined as test two.

7) Test to determine which length is smaller. If the test one result isshorter than the test result, the smaller circle is associated withP1_(X),P2_(Y), otherwise, the smaller circle is associated withP2_(X),P2_(Y).

8) Rename the variable associating to the size of the circle. See FIG.5B in which:

P1_(X),P2_(Y) =the beginning point of spline segment

P2_(X),P2_(Y) =the end point of spline segment

MNS=the normal slope of small circle segment, equivalent to MN1 or MN2depending on the relative results of test one and test two

MNL=normal slope of large circle segment

hs,ks=the center of the smaller of the two circle segments

hI,kI=the center of the larger of the two circle segments

P6_(X),P6_(Y) =a distance, defined by the radius of the small circle, toa point along MNL from the spline segment point associated with it

MNF=is the slope of the final line

9) Determine the intersection of the line described by slope of CNL andpassing through P3_(X),P3_(Y) and the line described by MNS through thespline segment point associated with it. The intersection point of thesetwo lines is the center of the smaller circle hs,ks.

10) Determine the Pythagorean distance from the small circle centerhs,ks to the spline segment points associated with it, This distance isthe radius of the small circle

11) Move along the line described by MNL and passing through the splinesegment point associated with it by the radius of the smaller circle rs.This point is P6_(X),P6_(Y).

12) Strike a line from P6_(X),P6_(Y) to hs,ks.

13) The negative inverse of the slope of the line from P6_(X),P6_(Y) andhs,ks is mnf.

14) Determine the midpoint of the line from P6_(X),P6_(Y) to hs,ks.

15) Determine the intersection of the line described by a slope of mnfand passing the point described in step 14 and the line described by MNLand through the spline segment point associated with it. Theintersection point of these two lines is the center of the larger circlehI,kI.

16) Determine the Pythagorean distance from the large circle centerhs,ks to the spline segment points associated with it. This distance isthe radius of the larger circle rI.

17) The intersection of the two circles is defined as the intersectionof the line going through the large circle center hI,kI and the smallcircle center hs,ks and either of the circles. At this point thetangency of the two circles are equivalent.

18) Accommodate an arc length calculation dependent upon which splinepoint is closer to P3_(X),P3_(Y) : If the test one result is greaterthan that of test two, then:

Theta1=ATN(m)-ATN(MSI)

Theta2=ATN(MLI)-ATN(m) otherwise:

Theta1=ATN(msI)-ATN(m)

Theta2=ATN(m)-ATN(mII)

where: ##EQU20## Theta1=the arc angle of the smaller circle Theta2=thearc angle of the larger circle.

19) Calculate arc length for each segment.

s1=rs(Theta1)

s2=rI(Theta2)

where:

s1=arc length of smaller segment

s2=arc length of larger segment

20) Calculate the running arc length.

21) Continue distally until all spline segments are converted.

FIGS. 5E-5J illustrate the building of the mandibular trough data pointsinto circle segments.

(2200) Tooth Placement on Curve Subroutine:

The individual tooth placement upon an equation is required in manysteps of the tooth finish position calculation procedure (94). Thepreferred method is described here in connection with the firstoccurrence in the procedure for the placement of the mandibular teeth.

There are four alternative equations upon which teeth can be placed: themandibular trough MT equation, the maxillary anterior arch form MAAFequation, the maxillary cuspid arch form MCAF equation, and the centralgroove marginal ridge arch form MGMRAF equation. All occlusion equationswill have been converted to circle segments before teeth are placed uponthem. A typical tooth placement is illustrated in FIG. 5N, in which:

DCP=Distal Contact Point

ICP=Incisal Center Point

MCP=Mesial Contact Point

MCPL=is the Mesial Contact Point Line.

The DCP is the point at which the tooth contacts the proceeding tooth.The ICP is the center of the tooth being placed. The MCP is the point atwhich the tooth contacts the preceding tooth. The MCPL is defined as theline through the DCP of the tooth being placed and the center of thecircle segment associated with the DCP. The MCPL is the line upon whichthe DCP of the proceeding tooth will be found.

The iterations to place the teeth onto the circle segments are:

1) Determine the offset distance for the mandibular central tooth on theside of the jaw under consideration.

2) Expand all circle segments about their centers by the offset amount.

3) Determine the intersection of the first circle segment and themidline. This is the mesial contact point MCP of the central, asillustrated in FIG. 5K.

4) Place the first circle C₁, whose radius is the mesio-distal width ofthe tooth, at MCP, as illustrated in FIG. 5K.

5) Determine which circle segment in the distal direction circle C₁intersects and identify the intersection point. This is accomplished byperforming an iteration which begins by transferring the coordinatesystem to the beginning point of the circle segment, as illustrated inFIG. 5L, in which:

X_(BEG),Y_(BEG) =beginning coordinates of the circle segment

X_(END),Y_(END) =End points of the circle segment

X_(INT),Y_(INT) =coordinates of circle intersection

X and Y axes are oriented at X_(BEG),Y_(BEG),

The two following circle equations are then solved simultaneously:

    R.sub.1.sup.2 =(x-h1)+(y-k1)

    R.sub.2.sup.2 =(x-h2)+(y-k2)

Where:

h1,k1=the center coordinates of the first circle

h2,k2=the center coordinates of the second circle

R₁ =the radius of the first circle C₁

R₂ =the radius of a second circle C₂

X,Y=coordinates of possible intersection points

The following solutions are possible: (1) two real solutions which arelabeled X1_(INT),Y1_(INT) and X2_(INT),Y2_(INT), respectively. (2)imaginary solutions, which are discarded, whereupon the next circlesegment is evaluated. If intersections are real, the circle segment isrotated, as illustrated in FIG. 2M, such that X_(END),Y_(END) is placedon the X axis. Then, X_(BEG),Y_(BEG) is subtracted from the rotated Xintersection point X1_(INT) or X2_(INT), and rotated X_(END) issubtracted from the rotated X intersection point X1_(INT) or X2_(INT).If the signs of the results of the two subtractions are opposite, therotated intersection point is tested for a value less than zero. If itis not less than zero, the other rotated intersection point is tested todetermine if it is valid. The testing continues until a segment is foundsuch that the subtractions produce opposite sign results and theassociated rotated Y intersection point is less than zero. This is thedistal contact point DCP of the tooth, as illustrated in FIG. 5N.

6) Construct a line passing through the DCP and the center of the circlesegment that intersects C₁.

7) Place circle C₂, whose radius is one-half the mesio-distal width MDWof the tooth, at the MCP.

8) Determine which circle segment in the distal direction intersectscircle C₂ and identify the intersection point. This is the incisalcenter point ICP of the tooth, as illustrated in FIG. 5N.

9) Eliminate all expanded circle segments.

10) Determine the offset distance for the mandibular lateral.

11) Expand all circle segments about their centers by the offset amount.

12) Determine the intersection point of the expanded circle segment ECSassociated with the DCP MCP Line. The intersection point is the mesialcontact point MCP of the lateral, as illustrated in FIG. 5O.

13) Place circle C₁, with radius the mesio-distal width MDW of thelateral, at the current MCP point.

14) Determine which circle segment in the distal direction circle C₁intersects and identify the intersection point, which is the DCP of thelateral.

15) Construct a line passing through the DCP and the center of thecircle segment that intersects C₁.

16) Place circle C₂, whose radius is one half the mesio-distal width MDWof the tooth, at the MCP.

17) Determine which circle segment in the distal direction intersectscircle C₂ and identify the intersection point. This is the incisalcenter point ICP of the tooth, as illustrated in FIG. 5P.

18) Continue distally until all teeth are placed.

19) Perform the same iterations for the co-lateral side of the arch.

(97) Appliance Manufacturing Procedure

The appliance manufacturing procedure (97) includes the steps of (3000)manufacture of the custom brackets, (3200) manufacture of the customarchwires and (3500) manufacture of custom placement jigs for placementof the custom brackets on the patient's teeth. These steps are describedin detail below for the embodiment in which all of the manufacturing iscarried out at the appliance design facility 13.

(3000) Bracket Manufacturing Step:

The bracket manufacturing step (3000) produces the custom brackets,preferably by selecting bracket blanks and cutting a torque slot in thebracket for the archwire 64. This utilizes the modified CNC mill 40illustrated in FIG. 2D. The bracket slot cutting step is illustrated inthe detailed flowchart of FIG. 2X.

Referring to FIG. 2X, the bracket manufacturing step (3000) begins withthe computer 30c (3005) loading the data for each bracket from thepatient data file 36.

For each tooth and bracket, as a default or initial selection, (3010)low profile brackets are assumed. Then, the slot angle FAI and the slotin-out dimension IO are read. Also, (3020) the radius of the archwire atthe tooth midpoint is determined.

Then, (3025) a main CNC program is created and (3030) the program loopsto generate the code for the cutting of each bracket, beginning with thecalculation of the variables for the bracket, (3040) assigning thevariables for each bracket to (3045)-(3050) set the cutting of the slotat the appropriate angle by rotating the bracket support 73 and settingthe cutter 77c to a cooperating height Z and horizontal X position. Ifthe position of the slot lies outside of the area of the bracket, abracket of the appropriate higher profile is called for by the program,and loaded, either automatically or by an operator. The code is thengenerated (3055) to control the path of the cutter in the Y direction tocut the archwire radius in the slot bottom. (3060) then, the NC code iscombined with the calculated variable values for the tooth and bracketand a subroutine is generated for the bracket, with (3065) the P-codessubroutines written the file. (3068) The program loops until codes forall of the brackets are complete.

Then, (3070) the CNC code is preferably downloaded to an NC controllerand the brackets are formed by the cutting of the slots in the series ofbracket blanks, and (3080) a report is written.

(3200) Archwire Manufacturing Step:

The archwire manufacturing step (3200) produces the archwire 64, asillustrated in FIG. 2E, preferably that is symmetrical about itsarchwire midline AML, having the appropriate terminal leg span TLS,formed of a series of circle segments.

As illustrated in the flowchart of FIG. 2Y, the archwire manufacturingstep (3200) executes a program with the manufacturing control computer30c to generate a CNC code to operate the wire forming machine 40. Theprogram begins by (3215) opening one or more files from the calculatedpatient data 36 and reads therefrom the wire alloy and the wirecross-section prescribed, and an array of data that contains a series ofj sets of data including the radius and sector length of each circlesegment of which the archwire curve is formed, and the calculated totalcumulative archwire length. To the archwire equation, (3220) a radii andsector lengths are added to produce a one-half inch of straight segmentat each end of the wire to form parallel terminal leg extensions. Then,calculating the cumulative slopes and sector lengths of the wire alongthe equation, (3225) the terminal leg span TLS is calculated.

Based upon the wire type selected, (3230) one of several data files ortables are read. For rectangle wire, for example, four files wouldinclude: (1) 0.022" thickness stainless steel (SS), (2) 0.025" thicknessSS, (3) 0.022" thickness titanium molybdenum alloy (TMA), and (4) 0.025"thickness TMA. Other files are provided for round wires of variousdiameters and types.

Then, using the cubic spline subroutine (2000), (3235) the slopes of thecubic spline equation describing wire behavior are calculated by: (1)computing the coefficients of a parabola, (2) filling the first point ofa slope array, (3) filling the intermediate points of the slope array,and (4) filling the last point of the slope array. Then, (3240) thecubic spline coefficients are calculated. Then, (3245) the verticaldisplacement of the bending lever arm LA (FIG. 2E) between the contactpoints of the roller 70b with the wire 69 and the contact point of therollers 68 with the wire 69 is determined for each circle segment of thearchwire equation, and data added to the array.

Then, (3255) temporary variables are defined for the sector length,lever arm displacement, radius and terminal leg span across the straightsegments of the archwire, (3260) the controller card 65 of the computer30c is initialized, (3265) the controller base address is set, and(3270) default parameters are set. Then, (3275) a sequential series ofsector lengths and lever arm displacements are sent respectively (1)through the circuits 66a and 67a to the drive of the feed rolls 68, and(2) through the circuits 66b and 67b to the anvil assembly 70.

When all circle segments have been formed, (3280) the lever armdisplacement is zeroed and (3285) the wire leg location is read by thesensor 71. This reading converted to a numerical value in the computer30b and any difference in the actual measured terminal leg span and thedesired terminal leg span TLS is calculated. If (3290) the difference isout of tolerance, a correction is made and another wire is formed.

(3500) Jig Manufacturing Step:

The jig manufacturing step (3500) produces bracket placement jigs customdesigned for each tooth to aid in the placement of the custom designedbrackets in the proper positions on the teeth so that the customdesigned archwire will, when installed in the custom designed and customplaced brackets, move the teeth to their calculated finish positions.

The information necessary for the design of the custom placement jigs iscontained in the patient data file of from the calculations made in theappliance design procedure (96) and in the tooth profile data file ofdigitized information read in step (500), in the illustrated embodimentof the invention. The design of the custom jigs involves, primarily, anassembly of the information already generated, and, in the preferredembodiment, takes place in the course of generating the code for controlof the NC controlled manufacturing equipment 41 that produces the jigs.

In the preferred and illustrated embodiment, the jig manufacturingequipment 41 is a standard CNC mill equipped with a small carbideendmill tool of, for example, 0.020 inches in diameter (FIG. 1F). Thejigs themselves 82 are made from circular ABS plastic wafers 83 ofapproximately one inch in diameter and approximately 0.040 inches inthickness, though considerable variation in size is acceptable.

The jig manufacturing step (3500), as illustrated in the detailedflowchart of FIG. 2Z, begins with the execution of a program or routinein the manufacturing computer 30b and the input of parametersidentifying the patient or case. Upon beginning of the execution of theprogram, (3515) the file of patient data 36 generated in the toothposition calculation and analysis procedure (95) and the appliancedesign procedure (96) is opened and information is read for each tooth,as illustrated in the diagram of FIG. 9I, in relation to a tooth profilePF. The variables read are (a) the intersection of the archwire planeand the labial (or lingual, if prescribed) surface of the tooth TS,which is in the form of a pair of X, Y coordinates TS_(X),Y in the toothprofile vertical-labial/lingual plane, (b) the slot in-out dimensionElan or IO, (c) the type of bracket, which provides access to theappropriate place in a lookup table of bracket dimensions, such asbracket base thickness BReI and bracket pad height BPH, and (d) thetorque slot width, 0.018 or 0.022 from the prescription.

Then, (3520) the bracket data file is opened and the bracket basethickness read, as illustrated in FIG. 9J. Then, a file name isassigned, (3530) a CNC file is created, and (3535) a CNC "main" programis written to it, as set forth, for example, in the flowchart of FIG.2Z-1.

Then, (3540) a sequential file is identified that contains the beginningand ending object number for each tooth profile, and (3545) a CADprogram file containing the tooth profiles PF_(I) is loaded. Theprofiles PF, as illustrated in FIG. 3C, are made up of a series ofclosely spaced points in the profile plane, each represented by X,Ycoordinates, connected by straight line segments to define the profilecurve PF. The endmill tool diameter is also entered, which must be lessthan the archwire diameter or archwire slot width (0.018 or 0.022).Constants are declared, including the diameter of the jig blank 83, thecut clearance on the outside of the jig, the number of loops, set at 23,and the counter initial settings.

Then, (3560) the CNC P-code is generated for each tooth, by loopingthrough substeps (3560) through (3639) until the code for each of thejigs 82 is generated. The loop begins by (3560) incrementing the toothand P-code counters by 1. The loop begins with the lower left bicuspid,as brackets are usually not used on the molars, and proceeds left toright. Thus, (3565), when the incrementing of the counter advances thecount to the lower right molar, (3565) the counter is advanced to skipto the upper left bicuspid.

Then, (3570) the parameters for the particular tooth are set up asillustrated in the flowchart detail of FIG. 2Z-2. This is followed bycreating the profile and bracket clearance compensation tool paths ITPand BCTP, respectively, as illustrated in the flowchart detail of FIG.2Z-3. This involves (3590) the creation of an initial inside tool pathline IITP made up of a series of straight line segments, one parallel toeach of the line segments of the tooth profile curve, spaced a distanceequal to the tool radius on the inside of the profile curve, asillustrated in FIG. 9K, (3595) the creation of an initial bracket basecompensation tool path line IBCTP made up of a series of straight linesegments, one parallel to each of the line segments of the tooth profilecurve, spaced a distance equal to the bracket base dimension minus thetool radius outside of the profile curve, as illustrated in FIG. 9L, and(3600) creation of the final bracket base compensation tool path (d) tocut from the inside tool path line to the base compensation line at thetop of the bracket base pad to cut off the jig at the bottom of the pad,as illustrated in FIG. 9M ("top" and "bottom" being used as an examplefor the lower teeth, and being opposite for the upper teeth).

Next, (3605) the archwire slot tool path ASTP is created as illustratedin the flowchart detail of FIG. 2Z-4, which can be understood from thesequence set forth in the flowchart with reference to the diagrams ofFIGS. 9N, 9O and 9P. Then, as set forth in the flowchart detail of FIG.2Z-5, (3610) a reference tool path RefP is created on an image of a jigblank 83, as illustrated in FIG. 9Q, and with reference to it, (3615)the outside jig boundary cutout CTP is added as illustrated in FIG. 2R,and (3620) the actual tool path TP is then generated as illustrated inFIG. 9S.

Then, (3625) the CNC machine code is generated, as illustrated in thedetailed flowchart of FIG. 2Z-6, and written to the output file. Then,(3630) the variables are reset, (3635) the final results are displayed,and (3640) the program loops back to substep (3560) until all of thebracket jig code have been generated. Then, (3645) the completed CNCfile is sent to the controller of the CNC mill and a pallet of wafers83a (FIG. 1F) is cut into a set of bracket placement jigs 82. An exampleof one of the jigs is illustrated in FIGS. 9T through 9W.

What is described above includes the preferred embodiments of theinvention. Those skilled in the art will appreciate that additions toand modifications of the system and method of the invention, and thedetailed manifestations thereof, may be made without departing from theprinciples of the inventive concepts set forth herein.

Accordingly, the following is claimed:
 1. An apparatus for manufacturinga custom orthodontic appliance, the apparatus comprising:a scanner forgenerating data signals containing information of anatomical shapes froman individual patient's mouth; a computer programmed to automaticallyderive a dental archform for the individual patient, to calculate finishpositions of the teeth of the patient in relation to the archform, tocalculate a custom orthodontic appliance design for placement on theteeth of the patient to move the teeth of the patient to the calculatedfinish positions on the derived dental archform, to produce machinereadable records of the calculated appliance design; an automatedfabricating machine controlled to respond to the machine readablerecords to fabricate a custom orthodontic appliance for the individualpatient having the calculated custom orthodontic appliance design. 2.The apparatus of claim 1 wherein:the scanner is operative to generatethe data signals to contain information of shapes of the patient's teethand of the shape of the patient's lower jaw; the computer is programmedto automatically derive the dental archform for the individual patientbased on the shape of the patient's lower jaw and to calculate thefinish positions of the teeth of the patient and the custom orthodonticappliance design based at least in part on the shape of the patient'steeth.
 3. An apparatus for manufacturing a custom orthodontic bracketincluding a bracket base having a mounting surface securable to a toothof a patient and an archwire support fixed to and extending from thebracket base and having an archwire receiving slot therein, theapparatus comprising:a holder having means thereon for mounting abracket blank thereon for fabrication; means for recording digitalinformation related to the individual anatomy of the patient thatrepresents the orthodontic positioning of the teeth of the patient;means for calculating from the digital information the geometry oforthodontic brackets of an orthodontic appliance for orthodonticallypositioning the teeth of the patient, including calculating geometricrelationships of the slots of the brackets to the mounting surfaces ofthe bracket bases of the respective brackets; means for forming at leastone surface of a bracket blank mounted on the holder in response to amachine control signal communicated thereto; and means for generatingfrom the calculated bracket geometry and communicating to the formingmeans a machine control signal for shaping the bracket blank mounted onthe holder to produce a bracket having a slot of the calculatedgeometric relationship to the mounting surface of the bracket basethereof.
 4. The apparatus of claim 3 wherein:each slot includesgenerally parallel upper and lower sides defining a slot inclination andincludes a slot base at an end thereof nearest the bracket base defininga slot position; each calculated geometric relationship of a slot to themounting surface of a bracket includes the slot inclination and a slotposition relative to the mounting surface; and the generated machinecontrol signal carries machine control instructions for causing theforming means to shape the bracket blank to produce a bracket having aslot of the calculated slot inclination and slot position with respectto the mounting surface.
 5. The apparatus of claim 4 wherein:the slot ofeach bracket is adapted to receive an archwire having a custom curvatureadjacent the tooth on which the bracket is to be secured; and eachcalculated geometric relationship of a slot to the mounting surface of abracket includes a slot bottom curvature conforming to the customcurvature of the archwire adjacent thereto; and the generated machinecontrol signal carries machine control instructions for causing theforming means to shape the bracket blank to produce a bracket having aslot of the calculated slot bottom curvature.
 6. The apparatus of claim5 wherein:the forming means includes means for cutting a slot in thesupport in response to the control signal; the calculating meansincludes means for defining an archwire plane that intersects a bracketwhen mounted on a tooth; and the apparatus further comprises means forangularly orienting and translating the holder with respect to theforming means so that the cutting means will operate in response to thecontrol signal to cut a slot in the support of a blank mounted on theholder and lying along the intersection of the archwire plane with thebracket with a slot bottom having the slot bottom curvature.
 7. Theapparatus of claim 4 wherein:the calculating means includes means fordefining an archwire plane that intersects a bracket when mounted on atooth; and the apparatus further comprises means for angularly orientingand translating the holder with respect to the forming means so that theforming means will operate in response to the control signal to cut aslot in the blank mounted on the holder that lies along the intersectionof the archwire plane with the bracket with the sides of the slotparallel to the archwire plane at the slot inclination to the mountingsurface of the bracket base and to the depth of the slot position withrespect to the mounting surface of the bracket base.
 8. The apparatus ofclaim 3 wherein:the forming means includes means for cutting a slot inthe bracket base in response to the control signal.
 9. The apparatus ofclaim 8 wherein:the forming means includes means for cutting a slot inthe bracket blank in response to the control signal; and the cuttingmeans includes a mechanical slot cutting element moveable with respectto the holder to cut in the bracket blank a slot of the slot inclinationand slot position with respect to the mounting surface of the bracketbase.
 10. The apparatus of claim 8 wherein:the calculating meansincludes means for defining an archwire plane that intersects a bracketwhen mounted on a tooth; and the apparatus further comprises means forangularly orienting and translating the holder with respect to theforming means so that the cutting means will operate in response to thecontrol signal to cut a slot in the support of a blank mounted on theholder and lying along the intersection of the archwire plane with thebracket with the sides of the slot parallel to the archwire plane at theslot inclination to the mounting surface of the bracket base and to thedepth of the slot position with respect to the mounting surface of thebracket base.
 11. The apparatus of claim 3 wherein:the holder and theforming means are mounted on a stand; and the apparatus furthercomprises means for angularly orienting the holder with respect to thestand and to the forming means, and means for translating the formingmeans with respect to the stand and to the holder, in response to thecontrol signal.
 12. The apparatus of claim 3 wherein:means for comparingthe geometry of each of the brackets to bracket blank criteria and forselecting therefrom an optimum one of a plurality of bracket blanks forthe fabrication of the bracket.
 13. A custom orthodontic archwiremanufacturing apparatus comprising:an archwire former including meansfor forming a length of orthodontic archwire material into a controlledshape in response to a wire shape control signal communicated thereto;means for producing a digitized record of anatomical shapes of anindividual patient's mouth; and a digital computer including programmeans responsive to the digitized record for deriving digital archwireshape data based on the digitized record, the computer further includingmeans for generating a wire shape control signal in response to thedigital archwire shape data, such that, when the signal is communicatedto the archwire former, the former will produce a custom orthodonticarchwire conforming to the anatomical shape of the individual patient'smouth.
 14. The apparatus of claim 13 wherein:the derived digitalarchwire shape data includes wire length data correlated to a lengthcomponent of the derived digital archwire shape data and wire curvaturedata correlated to a curvature component of the derived digital archwireshape data that is a function of the length component; the wire shapecontrol signal includes a wire feed control signal carrying the wirelength data and a wire bending control signal carrying the wirecurvature data; means for generating the wire feed control signal andmeans for generating a wire bending control signal and communicating thecontrol signals to the archwire former; and the archwire former includesmeans for longitudinally feeding the orthodontic archwire material inresponse to the wire feed control signal and means for transverselybending the archwire material fed by the wire feeding means in responseto the wire bending control signal and in synchronism with the feedingof the archwire material.
 15. The apparatus of claim 13 wherein:thedigital archwire shape data is a digital representation of a connectedseries of wire segments, each having a length component and a curvaturecomponent; and the archwire former includes means for longitudinallyfeeding a series of lengths of the orthodontic archwire materialcorresponding to the respective wire length components in accordancewith the wire length data and means for bending each fed length ofarchwire material to a curvature corresponding to the respective wirecurvature component in accordance with the wire curvature data.
 16. Theapparatus of claim 15 wherein:each wire segment is in the form of acircle segment with the length component thereof representing atangential length of archwire material and with the curvature componentthereof representing a constant radius of curvature of the material overthe tangential length of the segment; and the feeding means includesmeans for longitudinally feeding a series of tangential lengths of theorthodontic archwire material and the bending means includes means forbending each fed length of archwire segment to a constant radius inaccordance with the wire curvature data.
 17. The apparatus of claim 16wherein:the derived digital archwire shape data includes wire lengthdata correlated to a length component of the derived digital archwireshape data and wire curvature data correlated to a curvature componentof the derived digital archwire shape data that is a function of thelength component; the wire shape control signal includes a wire feedcontrol signal carrying the wire length data and a wire bending controlsignal carrying the wire curvature data; means for generating the wirefeed control signal and means for generating a wire bending controlsignal and communicating the control signals to the forming means; thefeeding means is operative to sequentially feed a series of lengths ofthe archwire material equal to the length components of the circlesegments, in response to the wire feed signal, along a longitudinalpath; the bending means includes a bending element moveable in responseto the wire bending control signal transverse to the path to impart atransverse bending deflection to the segment and a transverse positionsensor for producing a feedback signal responsive to the deflection; andthe computer includes means for modifying the wire bending controlsignal in response to the feedback signal to provide closed loop controlof the bending element.
 18. The apparatus of claim 17 wherein:theprogram means includes means in communication with the wire bendingcontrol signal generating means for receiving material property data ofthe archwire material and for modifying the wiring bending controlsignal in accordance with the property data to compensate for elasticproperties of the material.
 19. The apparatus of claim 18 furthercomprising:means for measuring an archwire span between points on firstand last segments of the series of the produced custom orthodonticarchwire; the program means including means for calculating a designarchwire span from the derived archwire shape data; means for comparingthe measured archwire span with the design archwire span and for storingthe results of the comparison; and the program means being operative togenerate the wire bending control signal in response to a stored resultof the comparison.
 20. The apparatus of claim 13 wherein:the programmeans comprises means for calculating preferred finish positions of thepatient's teeth from the digitized record and means for deriving thearchwire shape data in response to the calculated finish positions; andthe wire shape control signal generating means is operative to generatethe wire shape control signal which will produce a custom orthodonticarchwire that will urge the teeth toward the calculated finishpositions.
 21. The apparatus of claim 20 wherein:the program meansincludes means for deriving digital orthodontic bracket configurationdata that is related to the archwire shape data, to the calculated toothpositions and to the digitized record, for use in the fabrication oforthodontic brackets for connection of the custom archwire in thepatient's mouth.
 22. The apparatus of claim 21 wherein:the program meansincludes means for deriving the digital orthodontic bracketconfiguration data so as to optimize the shape of the archwire to aminimum of curvature inflection points.
 23. The apparatus of claim 22wherein:the digital archwire shape data is a digital representation of aconnected series of wire segments, each having a length component and acurvature component; each wire segment is in the form of a circlesegment the length component thereof representing a tangential length ofarchwire material and the curvature component thereof representing aconstant radius of curvature of the material over the tangential lengthof the segment; and the program means includes means for deriving thedigital orthodontic bracket configuration data so as to optimize theshape of the archwire to minimize the number of changes in radius fromlength to length.
 24. An apparatus for forming a jig for positioning abracket of a custom orthodontic appliance on a tooth of a patientcomprising:a jig former including means for shaping the contours of asurface of blank of jig forming material in response to a control signalcommunicated thereto; means for providing a digitized record of theshapes of the teeth of a patient and of the locations relative to thetooth shape record of appliance connection points on surfaces of theteeth; means for calculating, from the digitized tooth shape andconnection point record, jig geometry defining a jig locating surfacethat conforms to a unique portion of the external surface of the crownof a tooth, and defining an appliance engaging surface having the samelocation relative to the jig locating surface as the unique portion ofthe external surface has to the connection point on the tooth; means forgenerating a machine control signal carrying machine controlinstructions for producing a jig in accordance with the calculated jiggeometry; and control means for operating jig former in response to thecontrol signal.
 25. The apparatus of claim 24 wherein:the applianceincludes a plurality of brackets, one for connection at each connectionpoint to a tooth; the apparatus further comprises means for providingdigitized bracket shape data of an external surface of each bracket tobe connected to a connection point; and wherein the jig geometrycalculating means includes means for defining the appliance engagingsurface of the jig to conform, in response to the digitized bracketshape data, to the established appliance geometry.
 26. The apparatus ofclaim 25 wherein:each bracket has an archwire receiving slot therein;the bracket shape data includes a digital representation of the positionand inclination of the slot in the bracket; and the jig geometrycalculating means includes means for defining the appliance engagingsurface to include a part thereof that will align with the slot of thebracket when the bracket is engaged thereby.
 27. The apparatus of claim26 wherein:the appliance engaging surface includes a separate guidemember dimensioned to fit in the slot of the bracket and to engage thepart of the appliance engaging surface to hold slot of the bracketrelative to the jig at a desired position and inclination.
 28. Theapparatus of claim 24 further comprising:means for supporting a blank ofjig forming material; the machine includes a cutting tool operative inresponse to the control signal to cut the defined surfaces of the jiginto the blank in accordance with the machine control instructions.